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Nuclear Import Receptor Inhibits Phase Separation of FUS through Binding to Multiple Sites.Yoshizawa, T., Ali, R., Jiou, J., Fung, H.Y.J., Burke, K.A., Kim, S.J., Lin, Y., Peeples, W.B., Saltzberg, D., Soniat, M., Baumhardt, J.M., Oldenbourg, R., Sali, A., Fawzi, N.L., Rosen, M.K., Chook, Y.M. (2018) Cell 173: 693-705.e22 - PubMed: 29677513 - DOI: 10.1016/j.cell.2018.03.003 - Primary Citation of Related Structures: 5YVG, 5YVI, 5YVH - PubMed Abstract: Liquid-liquid phase separation (LLPS) is believed to underlie formation of biomolecular condensates, cellular compartments that concentrate macromolecules without surrounding membranes. Physical mechanisms that control condensate formation/dissolutio ... Liquid-liquid phase separation (LLPS) is believed to underlie formation of biomolecular condensates, cellular compartments that concentrate macromolecules without surrounding membranes. Physical mechanisms that control condensate formation/dissolution are poorly understood. The RNA-binding protein fused in sarcoma (FUS) undergoes LLPS in vitro and associates with condensates in cells. We show that the importin karyopherin-β2/transportin-1 inhibits LLPS of FUS. This activity depends on tight binding of karyopherin-β2 to the C-terminal proline-tyrosine nuclear localization signal (PY-NLS) of FUS. Nuclear magnetic resonance (NMR) analyses reveal weak interactions of karyopherin-β2 with sequence elements and structural domains distributed throughout the entirety of FUS. Biochemical analyses demonstrate that most of these same regions also contribute to LLPS of FUS. The data lead to a model where high-affinity binding of karyopherin-β2 to the FUS PY-NLS tethers the proteins together, allowing multiple, distributed weak intermolecular contacts to disrupt FUS self-association, blocking LLPS. Karyopherin-β2 may act analogously to control condensates in diverse cellular contexts. Department of Pharmacology, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA; Howard Hughes Medical Institute (HHMI) Summer Institute, Marine Biological Laboratory, Woods Hole, MA 02543, USA. Electronic address: [email protected].

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http://onhomeworkqchn.presidentialpolls.us/applicatios-of-geometry.html

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Geometry has many practical applications in everyday life area and volume of geometric figures geometry : polygons, real-life applications of right triangles, volume of a pill capsule. Applications of geometry in the real world include computer-aided design for construction blueprints, the design of assembly systems in manufacturing, nanotechnology, computer graphics, visual graphs. Topic: real life applications- applications of coordinate geometry- application question 4 subject: mathematics grade: ix in this video we solve a question. Geometry and its applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric. Architecture is one of the applications of geometry that is crucial because architects are responsible for building sound structures and they must use geometric components to do so. In this tutorial we discuss the related problems of application of geometric sequence and geometric series example: a line is divided into six parts forming a geometric sequence. Principal of geometry and some applications of crystal structure in materials karimat el-sayed physics departement, faculty of science, ain shams university whatis. Applications of computational geometry in my work at mentor graphics, i have applied computational geometry algorithms and concepts on several occasions. Euclidean geometry introduction geometric definitions euclidean geometryapplications of geometry geometry is everywhere around us - in nature, architecture, technology and design. Transverse linechapter 10 applications of geometry and trigonometry 463 some geometry (angle) laws the following angle laws will be valuable when finding unknown values in the applications to be. Using glencoe geometry: concepts and applications, you can: help students obtain better understanding of geometry with the many detailed examples and clear and concise explanations. Applications of geometry modeling preparation of geometry models for meshing is essential to all mesh types. Applications of fractal geometry an honors project at the university of rhode island, spring when i began this project, i had almost no knowledge of fractal geometry i had to learn some basic. [summary]practical applications for geometry some practical applications of elementary geometry login via openathens search for your institution's name below to login. Before you tell me that this question has been asked, give me a bit of your time please to read this question because it is not as simple as it sounds. Applications of geometry despite all of the different subject areas of mathematics that exist, perhaps geometry has the most profound impact on our everyday lives. The applications of geometry in real life are not always evident to teenagers, but the geometry was recognized to be not just for mathematicians anyone can benefit from the basic learning of. Applications of geometry 1 geometry in real life 2 definition noun merriam-webster dictionary a 18 a graphic designer studies how basic geometric shapes combine into artistic visual layouts in two. Before exploring applications of fractal geometry in ecology, we must first define fractal geometry a mathematician who works in the field of geometry is called a geometer. The international journal of computational geometry and applications (ijcga) is a bimonthly journal published since 1991, by world scientific it covers the application of computational geometry in design and analysis of algorithms. Applications of hyperbolic geometry mapping the brain spherical, euclidean and hyperbolic geometries in mapping the brain all those folds and fissures make life difficult for a neuroscientist. Geometry is a one of the important study of mathematics it is foundation for learning geometry objects (two dimensional objects, three dimensional objects)geometry is study of size and shapes of an. There are tons of real life applications of geometry geometry is defined as the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids. Geometry & applications (ijcga) is a bimonthly journal devoted to the field of computational geometry within research findings or experiences in the implementations of geometric algorithms. Geometrical applications of calculus (1 of 4: an introduction to the applications of calculus) - продолжительность: 9:57 eddie woo 1 897 просмотров. Published by balkan society of geometers geometry balkan press, bucharest, romania i would like to recommend the balkan journal of geometry and its applications (issn 1224-2780. Topic: real life applications- applications of coordinate geometry- application question 4 topic: applications of coordinate geometry subject: mathematics grade: ix in this video we solve. Spherical geometry is also known as hyperbolic geometry and has many real world applications one of the most used geometry is spherical geometry which describes the surface of a sphere.

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https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2986630

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Optimizing Objective Functions Determined from Random Forests 46 Pages Posted: 16 Jun 2017 Last revised: 29 Jul 2020 Date Written: June 16, 2017 We study the problem of optimizing a tree-based ensemble objective with the feasible decisions lie in a polyhedral set. We model this optimization problem as a Mixed Integer Linear Program (MILP). We show this model can be solved to optimality efficiently using Pareto optimal Benders cuts. For large problems, we consider a random forest approximation that consists of only a subset of trees and establish analytically that this gives rise to near optimal solutions by proving analytical guarantees. The error of the approximation decays exponentially as the number of trees increases. Motivated from this result, we propose heuristics that optimize over smaller forests rather than one large one. We present case studies on a property investment problem and a jury selection problem. We show this approach performs well against benchmarks, while providing insights into the sensitivity of the algorithm's performance for different parameters of the random forest. Keywords: Random Forest, Optimization JEL Classification: C61 Suggested Citation: Suggested Citation

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http://computerescue.info/question-papers/james-stewart-multivariable-calculus-7th-edition-pdf-4141.php

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Maybe James Stewart Calculus 7th Edition Pdf Download PDF Calculus. They have all done an outstanding job. All of them have contributed greatly to the success of this book. Solution Builder www. Solution Builder allows you to create customized, secure solutions printouts in PDF format matched exactly to the problems you assign in class. ExamView Testing Create, deliver, and customize tests in print and online formats with ExamView, an easy-to-use assessment and tutorial software. ExamView contains hundreds of multiple-choice and free response test items. The Flash simulation modules in TEC include instructions, written and audio explanations of the concepts, and exercises. Selected Visuals and Modules are available at www. Enhanced WebAssign www. Instructors can further customize the text by adding instructor-created or YouTube video links. Additional media assets include: animated figures, video clips, highlighting, notes, and more! YouBook is available in Enhanced WebAssign. 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A Companion to Calculus By Dennis Ebersole, Doris Schattschneider, Alicia Sevilla, and Kay Somers ISBN X Written to improve algebra and problem-solving skills of students taking a Calculus course, every chapter in this companion is keyed to a calculus topic, providing conceptual background and specific algebra techniques needed to understand and solve calculus problems related to that topic. It is designed for calculus courses that integrate the review of precalculus concepts or for individual use. Linear Algebra for Calculus by Konrad J. Heuvers, William P. Francis, John H. Kuisti, Deborah F. Lockhart, Daniel S. Moak, and Gene M. Ortner ISBN This comprehensive book, designed to supplement the calculus course, provides an introduction to and review of the basic ideas of linear algebra. To the Student Reading a calculus textbook is different from reading a newspaper or a novel, or even a physics book. You should have pencil and paper and calculator at hand to sketch a diagram or make a calculation. Some students start by trying their homework problems and read the text only if they get stuck on an exercise. I suggest that a far better plan is to read and understand a section of the text before attempting the exercises. In particular, you should look at the definitions to see the exact meanings of the terms. Here you can find computational physics by newman shared files. There are books covering the areas of classical mechanics, thermodynamics, electromagnetism, optics, quantum physics, atomic and nuclear physics, astrophysics, and more. Every textbook comes with a day "Any Reason" guarantee. To obtain a solutions manual, please complete the form below, giving your name, email, and university affiliation. It contains a whole new chapter on the physics of music as well as several new sections such as those discussing the scaling in phase transitions, coupled nonlinear oscillators, two Find all the study resources for Computational Physics with Python by Mark Newman us to both broaden and deepen our understanding of physics by vastly increasing the range of mathematical calculations which we can conveniently perform. Download with Google Download with Facebook or download with email. Emphasis is given to methods based on Volterra series representations, the proper orthogonal decomposition, and harmonic balance. I would like to thank both of them sincerely for their interest, hospitality and many useful discussions while I was at Purdue. This web site contains resources that accompany the book Computational Physics by Mark Newman, including sample chapters from the book, programs and data used in the examples and exercises, the text of all the exercises themselves, and copies of all figures from the book. Solution and Testbank List 2 We have a huge collection of solutions and testbanks. We have been uploading solutions and testbanks but the product you are looking for may not have been uploaded yet. Bord Physics for Scientists and Engineers Solution Manual 2nd Edition A Strategic Approach with Modern Final paper: review-type paper and in-class presentation on a current application of a statistical physics topic. This book provides an easy to read introduction covering many important topics. Computational physics can be represented as this diagram. We will be glad if you go back anew. 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I wanted to provide the students with a skill that they did not have to pay to use! It was roughly a month before my rst computational physics course be- Mark Newman Solutions. Different from the previous edition is the decreased emphasis on decision-theoretic principles. Retaining the style of its previous editions, this text presents the theory, computational aspects, and applications of vibrations in as simple a manner as possible. Use of the spatial kD-tree in computational physics applications. Barkema, Monte Carlo The MfS would also understand other frequencies to be down the sig-naling rejecting this description. Hence its primary audience is probably for undergraduate students however it can serve also as reference. And here are some additional resources from the author. In this paper, we review the development of new reduced-order modeling techniques and discuss their applicability to various problems in computational physics. This free book is a complete introduction to the field of computational physics, with examples and exercises in the Python programming language. The language had to be readily available on all major operating systems. Ivan Galeana. Problem 2. Limits and Continuous Functions21 1. Chapter 3, and the basic theory of ordinary differential equations in Chapter 6. Velocity and Distance. June 8, 3. Math is the third and the final part of our standard three-semester calculus sequence. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Students solve differential equations to find functions to model the value of a car in terms of its age. The graphs of the polar curves. It is open to others who are qualified and desire a more rigorous mathematics course at the core level. Introduction to Math Philosophy and Meaning. Consider the line L in the plane given by the equation 2x 5y 10 0. Notice that the axes are labeled differently than we are used to seeing in the sketch of D. Chapters 3 and 4 add the details and rigor. The Fundamental Theorem of Calculus 14 1. Most tests are given without answers. Calculus, 7th Edition This series is designed for the usual three semester calculus sequence that the majority of science and engineering majors in the United States are required to take. Erdman Background 3 1. This lesson course includes video and text explanations of everything from Calculus 3, and it includes quizzes with solutions! MIT Professor Gilbert Strang has created a series of videos to show ways in which calculus is important in our lives. Eventually I may penalize you for the failure to use full sentences. Functions8 4. The techniques of solving Double Integrals with a focus on how to construct a double integral over a given region. This page contains links to calculus tests offered at UAB in the past, according to the syllabus adopted at that time. Calculate the given quantity if Let u, v be in V3; that is, vectors of 3 components. This is a very condensed and simplified version of basic calculus, which is a prerequisite for many Math Calculus 3 Lecture Videos These lecture videos are organized in an order that corresponds with the current book we are using for our Math, Calculus 3, courses Calculus, with Differential Equations, by Varberg, Purcell and Rigdon, 9th edition published by Pearson. Write equations of lines and planes in space. The following video provides an outline of all the topics you would expect to see in a typical Multivariable Calculus class i. Concepts and Contexts, 4th ed. November 22, Rules for Finding Derivatives. Apply the concepts of calculus to vector-valued functions and use such functionsCalculus III Publisher: Cognella Date: English Pages: Here are a set of practice problems for the Calculus III notes. Either may be used for Calculus I and II. Please select one better suit your needs. Revision of vector algebra, scalar product, vector product 2. Computational physics newman solutions manual Rates of change17 5. Now make a further change of variables well adapted to the situation. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. The videos, which include real-life examples to illustrate the concepts, are ideal for high school students, college students, and anyone interested in learning the basics of calculus. MATH Stewart, J. All rights reserved. It was submitted to the Free Digital Textbook Initiative in California and will remain unchanged for at least two years. Classwork, 3 units; laboratory, 1 unit. Calculus III with applications. Does the value for pi have to be entered everytime it is used? Calculus Iii For Dummies Pdf 10 9 8 7 6 5 4 3 2. Typically, we have to Calculus I or needing a refresher in some of the early topics in calculus. These notes do assume that the reader has a good working knowledge of Calculus I …learn Calculus III or needing a refresher in some of the topics from the class. To make studying and working out problems in calculus easier, make sure you know basic formulas for geometry, trigonometry, integral calculus, and differential calculus. View Calculus 3 Textbook. I have tried to be somewhat rigorous about proving Calculus III: Practice Final Name: Circle one: Section 6 Section 7. Page 2. Then they compare their results with real data. Calculus I and II. What is Calculus 3? A Quick Overview. Shed the societal and cultural narratives holding you back and let free step-by-step Calculus Volume 3 textbook solutions reorient your old paradigms. The daily Here is the best resource for homework help with MAC This is the free digital calculus text by David R. Thomas Calculus 3 12th Edition Pdf. Calculus with Vector Functions. Harvard College Math 21a: Lamar University Number of pages: Homework consists of Level 1, Level 2, and Mixed Review problems. Write this number using the min notation. Basic properties of vector operations p. You may ask your instructor to check your answers if you use the test problems for practice. Eric Sullivan Calculus: Early Transcendentals, Briggs, First edition. The prerequisites are the standard courses in single-variable calculus a. Intuitive Idea Curvature is a measure of instantaneously how much a curve Introduction to Mathematica Calculus III In this lab, you will learn the basics of using Mathematica to evaluate expressions, plot functions and work with vectors. Topics include vectors, three-dimensional analytic geometry, partial differentiation and multiple integrals, and vector analysis.Derivatives and the Mean Value Theorem 3 4. Eventually I may penalize you for the failure to use full sentences. The study of networks received much interest in recent years. It explains the fundamentals of computational physics and describes in simple terms the techniques that every physicist should know, such as finite difference methods, numerical quadrature, and the fast Fourier transform. The College Board Subject: These skills are organized into categories, and you can move your mouse over any skill name to preview the skill. Students solve differential equations to find functions to model the value of a car in terms of its age. - FINANCIAL AND MANAGERIAL ACCOUNTING 17TH EDITION PDF - PRECALCULUS JAMES STEWART 5TH EDITION PDF - RITA MULCAHY CAPM EXAM PREP 3RD EDITION PDF - CCNA SECURITY LAB MANUAL VERSION 1.2 3RD EDITION EPUB - CALCULUS EARLY TRANSCENDENTALS 7TH EDITION SOLUTIONS MANUAL PDF - JAMES PATTERSON EPUB COLLECTION - PAUL DUBOIS MYSQL 4TH EDITION PDF - A POCKET STYLE MANUAL 6TH EDITION PDF - RULES COMPENDIUM 3.5 PDF - MICROSOFT POWERPOINT 2003 TUTORIAL PDF

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https://www.gemeinde-urnshausen.de/dealers/13077-retaining-wall-hydrostatic-pressure-formula.html

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Home / retaining wall hydrostatic pressure formula Hydrostatic Pressure on Basement Retaining Walls. What hydrostatic loading should be considered to act on the wall and how high up should the hydrostatic load be applied. Should hydrostatic pressure loading be considered to act all the way to the top of the wall, which is 19' above where the water table was measured at the time of the survey. Hydrostatic Force on a Wall: dp = g dz . 2.16 Integrating in the z-direction we get pressure as a function of depth: p = pa gz 2.19 Note that z is defined as zero at the surface, so pressure increases with depth since z < 0 under water with a constant slope, g . Pressure Computations. Last Revised: 11/04/2014. ASCE 7-05 3.2 treats both lateral soil loads and hydrostatic pressure similarly. Both increase linearly with depth according to the equation: lateral pressure at depth h = g h. This is common in cantilevered retaining walls. It becomes less so if the wall is restrained against movement in Definition. A retaining wall is a structure designed and constructed to resist the lateral pressure of soil, when there is a desired change in ground elevation that exceeds the angle of repose of the soil. A basement wall is thus one kind of retaining wall. But the term usually refers to a cantilever retaining wall, Retaining Wall Variables. Magnitude of stress or earth pressure acting on a retaining wall depends on: height of wall, unit weight of retained soil, pore water pressure, strength of soil angle of internal friction , amount and direction of wall movement, and. other stresses such as earthquakes and surcharges. Retaining Wall: Saturated Soil and Hydrostatic Pressure. Ask Question 2 The hydrostatic pressure and the soil load act on the wall concurrently. However, as you noted, the soil load is reduced because the effective weight of the soil is reduced due to buoyant forces. Percentage area of steel for a retaining wall - standard formula doesn't To understand how hydrostatic pressure can effect a retaining wall, one must fully understand the function of such a wall. Typically, a retaining wal l is a structure created from pre-cast or formed cement blocks that supports a mass of earth on one side in order to maintain two levels of elevation in one area. Finds the equivalent force and action point of hydrostatic pressure on a wall, which is an example of a distributed force. Distributed Force-Hydrostatic Pressure on Wall Darryl Morrell The thrust applied by water is considered to be acting at a distance of H/3 from the bottom of the retaining wall. The pressure distribution is triangular and has the maximum pressure of 2P/H at the bottom of the wall. hydrostatic pressure and dynamic water pressure acting on a structure should be calculated separately. 1 Earth Pressure Relating to Item 1 of the Public Notice Above Fig. 1.2.1 Schematic Diagram of Earth Pressure Acting on Retaining Wall CHAPTER 5 EARTH PRESSURE AND WATER PRESSURE. I am working on retaining wall structures Hydrostatic Pressure. Ron Structural 10 Aug 10 12:54. For water only, the pressure is unit weight of water * depth of water acting at 2/3 of the depth triangular pressure distribution The formula you showed for calculation the soil force, which i have to say is the resultant force comes from. What is the cause of hydrostatic pressure behind a retaining wall? How does hydrostatic pressure effect a retaining wall? What is the cause of hydrostatic pressure behind a retaining wall? How Earth Pressure and Retaining Wall Basics for Non-Geotechnical Engineers Richard P. Weber Course Content Content Section 1 Retaining walls are structures that support backfill and allow for a change of grade. For instance a retaining wall can be used to retain fill along a slope or it can be used to CHAPTER 9 EARTH PRESSURE AND HYDRAULIC PRESSURE - C9-1 - In general, earth pressure acting on a retaining wall is assumed to be active earth pressure, and is calculated by using, for example, Mononobe and Okabe's formula for active earth pressure during an earthquake. We know that water exerts a pressure on the wall and this thrust is calculated by using the following formula. P = ½Y o H 2 The thrust applied by water is considered to be acting at a distance of H/3 from the bottom of the retaining wall. The pressure distribution is triangular and has the maximum pressure of 2P/H at the bottom of the wall. Cantilever Retaining Walls: How to Calculate the Bearing Pressure By: Javier Encinas, PE July 25, 2017 A retaining wall is a structure exposed to lateral pressures from the retained soil plus any other surcharges and external loads. Another method for relieving hydrostatic pressure is to install a drainage pipe behind the wall. This should be a perforated pipe, to allow water to enter it through the length of the wall. The pipe can be located just above the footing, or can be located at a higher elevation. The retaining wall is checked for stability: Application of Lateral Earth Pressure Theories to Design Retaining Wall Stability 1 Safety Against Overturning Rotational stability : PV PH obtain cubic equation in terms of d. Solve for d. Increase d by 20% in quay walls.

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https://kiwylupuqytoguje.blackfin-boats.com/applied-engineering-mathematics-book-39167zd.php

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3 edition of Applied Engineering Mathematics found in the catalog. February 20, 2007 by Cambridge International Science Publishing Written in English |The Physical Object| |Number of Pages||336| This book offers the latest research advances in the field of mathematics applications in engineering sciences and provides a reference with a theoretical and sound background, along with case studies. In recent years, mathematics has had an amazing growth in engineering sciences. It forms the common foundation of all engineering disciplines. This new book provides a comprehensive range of. Higher Engineering Mathematics by B. S. Grewal. Highlights of the book: Good for undergraduate mathematics and GATE preparation. It covers all topics required for GATE and other exams. Theory, examples, problems are provided for each chapter. Best book for competitive exams; Essential Engineering Mathematics by Michael Batty. Highlights of the. Engineering mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and with fields like engineering physics and engineering geology, both of which may belong in the wider category engineering science, engineering mathematics is an interdisciplinary subject motivated by engineers' needs both for. When I was a college student, I saw a list of essential math books on a blog. I promised to myself to read all those books in 10 years because there were 50 books . Engineering Mathematics – I Dr. V. Lokesha 10 MAT11 8 Leibnitz’s Theorem: It provides a useful formula for computing the nth derivative of a product of two functions. Statement: If u and v are any two functions of x with u n and v n as their nth derivative. Then the nth derivative of uv is. that are needed in the course of the rest of the book. We treat this material as background, and well prepared students may wish to skip either of both topics. Elementary Topology In applied mathematics, we are often faced with analyzing mathematical structures as they might relate to real-world phenomena. A Textbook Of Practical Medicine V2 etre du balbutiement outline of social psychology Current trends in chemical engineering Bloodtrail to Mecca Rotations and angles Changing men, transforming culture Macraes Blue Bk 104/E The fall, & Exile and the kingdom. Electric transmission infrastructure and investment needs Medicine in its human setting The letters of Ralph Waldo Emerson Book Description Undergraduate engineering students need good mathematics skills. This textbook supports this need by placing a strong emphasis on visualization and the methods and tools needed across the whole of engineering. The visual approach is emphasized, and excessive proofs and derivations are avoided. This book can serve as a textbook in engineering mathematics, mathematical modelling and scientific computing. This book is organised into 19 chapters. Chapters introduce various mathematical methods, Chapters concern the numeri-cal methods, and Chapter 19 introduces the probability and by: 4. Hope this article Engineering Mathematics 1st-year pdf Notes – Download Books & Notes, Lecture Notes, Study Materials gives you sufficient information. Share this article with your classmates and friends so that they can also follow Latest Study Materials and Notes on Engineering : Daily Exams. Download Applied Mathematics - III By G.V. Kumbhojkar - The book has been rebinded and is useful for mechanical, automobile, production and civil engineering. "Applied Mathematics - III By G.V. Kumbhojkar PDF File" "Free Download Applied Mathematics. The books listed in this site can be downloaded for free. The books are mostly in Portable Data File (PDF), but there are some in epub format. Feel free to download the books. If you can, please also donate a small amount for this site to continue its Applied Engineering Mathematics book. Mathematics books Need help in math. Delve into mathematical models and concepts, limit value or engineering mathematics and find the answers to all your questions. It doesn't need to be that difficult. Our math books are for all study levels. Higher Engineering Mathematics is a comprehensive book for undergraduate students of engineering. The book comprises of chapters on algebra, geometry and vectors, calculus, series, differential equations, complex analysis, transforms, and numerical techniques. About the author () In books such as Introductory Functional Analysis with Applications and Advanced Engineering Mathematics, Erwin Kreyszig attempts to /5(8). Contour Deformation Morera’s Theorem. This book has been prepared by the Directorate of Technical Education This book has been printed on 60 G.S.M Paper Through the Tamil Nadu Text book and Educational Services Corporation Convener Thiru ENGINEERING MATHEMATICS. A First Course in Applied Mathematics is an ideal book formathematics, computer science, and engineering courses at theupper-undergraduate level. The book also serves as a valuablereference for practitioners working with mathematical modeling,computational methods, and the applications of mathematics in theireveryday work. Countless math books are published each year, however only a tiny percentage of these titles are destined to become the kind of classics that are loved the world over by students and mathematicians. Within this page, you’ll find an extensive list of math books that have sincerely earned the reputation that precedes them. For many of the most important branches of mathematics, we’ve. Applied Mathematics Applied mathematics involves mathematical methods used to solve practical problems in science, engineering, business, and industry. Dover offers foundational works, problem books, applied mathematics books, and more for engineers, physicists, and others. All are the lowest-priced editions available. Mathematics acts as a foundation for new advances, as engineering evolves and develops. This book will be of great interest to postgraduate and senior undergraduate students, and researchers, in engineering and mathematics, as well as to engineers, policy makers, and scientists involved in the application of mathematics in engineering. Application topics consist of linear elasticity, harmonic motions, chaos, and reaction-diffusion systems. This book can serve as a textbook in engineering mathematics, mathematical modelling and. The book's website provides dynamic and interactive codes in Mathematica to accompany the examples for the reader to explore on their own with Mathematica or the free Computational Document Format player, and it provides access for instructors to a solutions manual. Strongly emphasizes a visual approach to engineering mathematics. Engineering Mathematics with Examples and Applications provides a compact and concise primer in the field, starting with the foundations, and then gradually developing to Author: Xin-She Yang. The book’s website provides dynamic and interactive codes in Mathematica to accompany the examples for the reader to explore on their own with Mathematica or the free Computational Document Format player, and it provides access for instructors to a solutions manual. Strongly emphasizes a visual approach to engineering mathematicsPrice: $ Higher Engineering Mathematics by BS Grewal PDF is the most popular book in Mathematics among the Engineering Students. Engineering Mathematics by BS Grewal contains chapters of Mathematics such as Algebra and Geometry, Calculus, Series, Differential Equations, Complex Analysis, and the end of each chapter An exhaustive list of ‘Objective Type of. Physical Sciences and Engineering; Mathematics; Books in Mathematics; Books in Mathematics. Our wide variety of books and eBooks has been empowering research development, initiating innovation, and encouraging confidence and career growth in the scientific field of Mathematics. Discover Mathematics books. The source of all great mathematics is the special case, the con-crete example. It is frequent in mathematics that every instance of a concept of seemingly great generality is in essence the same as a small and concrete special case.1 We begin by describing a rather general framework for the derivation of PDEs.Engineering Mathematics II Appled Mathematics. Each chapter of this book is presented with an introduction, definitions, theorems, explanation, solved examples and exercises given are for better understanding of concepts and in the exercises, problems have been given in view of enough practice for mastering the concept.Mathematics for Circuits by W. Chellingsworth Mechatronic Systems Design Methods, Models, Concepts by Klaus Janschek Electrical Inspection, Testing and Certification A Guide to Passing the City and Guilds Exams Third Edition by Michael Drury.

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CC-MAIN-2022-33

https://lambdageeks.com/how-to-find-tangential-acceleration/

math

In the world of physics and mathematics, understanding the concept of tangential acceleration is crucial. It plays a significant role in analyzing the motion of objects in circular or rotational motion. In this blog post, we will explore the concept of tangential acceleration in detail, including its definition, importance, and how to calculate it in various scenarios. So, let’s dive in! How to Find Tangential Acceleration Definition of Tangential Acceleration tangential acceleration refers to the rate at which the tangential velocity of an object changes over time in a circular or rotational motion. It is a measure of how quickly an object’s speed or direction changes along the circular path it follows. In simple terms, it represents the acceleration experienced by an object moving in a circle. Importance of Tangential Acceleration in Physics and Mathematics tangential acceleration is essential in understanding the dynamics of rotational motion. It helps us analyze and predict how objects move in circular paths, such as planets orbiting the sun, cars taking turns on a racetrack, or even the motion of a spinning top. By considering tangential acceleration, we can determine the forces acting on an object, its velocity, and how it responds to external influences. The Formula to Find Tangential Acceleration The formula to calculate tangential acceleration depends on various factors, including angular acceleration, time, and linear velocity. It can be expressed as: – represents the tangential acceleration – is the radius of the circular path – denotes the angular acceleration Now that we have a clear understanding of tangential acceleration let’s explore how to calculate it in different scenarios. How to Calculate Tangential Acceleration Calculating Tangential Acceleration from Angular Acceleration To calculate tangential acceleration from angular acceleration, we can use the formula mentioned earlier: . Let’s consider an example to illustrate this: Suppose a particle is moving in a circular path with a radius of 3 meters, and it experiences an angular acceleration of 2 rad/s². To find the tangential acceleration, we can apply the formula: Hence, the tangential acceleration is 6 m/s². Finding Tangential Acceleration Given Time Sometimes, we may need to calculate tangential acceleration when the time is given. In such cases, we can use a different formula based on the initial angular velocity, the angular acceleration, and the time. The formula is: – (a_t) represents the tangential acceleration – (\omega_0) is the initial angular velocity – (\alpha) denotes the angular acceleration – (t) is the time Let’s consider a scenario where an object starts from rest and experiences an angular acceleration of 5 rad/s² for a duration of 2 seconds. The initial angular velocity is 0. By substituting the given values, we can calculate the tangential acceleration: Hence, the tangential acceleration is 10 m/s². Determining Tangential Acceleration Without Time In some cases, we may need to determine the tangential acceleration without knowing the time duration. In such situations, we can use equations that involve the angular velocity , the radius (r), and the tangential acceleration (at). One such equation is: Suppose an object is moving in a circular path with a radius of 2 meters and has an angular velocity of 3 rad/s. To find the tangential acceleration, we can use the formula: Therefore, the tangential acceleration is 18 m/s². Now that we have covered the basics of calculating tangential acceleration, let’s explore how to solve it in different scenarios. How to Solve for Tangential Acceleration in Different Scenarios Finding Tangential Acceleration in Circular Motion When dealing with circular motion, tangential acceleration is an important parameter to consider. It helps us understand how objects accelerate along the circular path. In circular motion, tangential acceleration is always directed towards the center of the circle. The magnitude of tangential acceleration depends on factors like angular acceleration, radius, and linear velocity. Determining Tangential Acceleration of a Pendulum A pendulum is an excellent example where tangential acceleration comes into play. When a pendulum swings back and forth, the bob experiences tangential acceleration. The magnitude of tangential acceleration is determined by the length of the pendulum, the angle it swings, and the gravitational acceleration. Calculating Tangential Acceleration in Vertical Circular Motion In vertical circular motion, the tangential acceleration helps us understand how objects accelerate or decelerate as they move up or down along the circular path. The tangential acceleration in vertical circular motion varies depending on the location of the object in the circular path. At the topmost point, the tangential acceleration is directed downward, while at the bottommost point, it is directed upwards. How to Find Tangential Velocity and Speed with Centripetal Acceleration Finding Tangential Velocity with Centripetal Acceleration and Radius tangential velocity represents the linear velocity of an object moving along a circular path. It is related to centripetal acceleration (the acceleration towards the center of the circle) and the radius of the circular path. The formula to calculate tangential velocity is: – represents the tangential velocity – is the centripetal acceleration – denotes the radius Calculating Tangential Speed with Centripetal Acceleration tangential speed refers to the magnitude of the tangential velocity. It represents how fast an object is moving along a circular path. To calculate tangential speed, we need to know the tangential acceleration and the time it takes for the object to complete one revolution around the circle. The formula for tangential speed is: – represents the tangential speed – is the tangential acceleration – denotes the time How to Find Tangential Component of Linear Acceleration Finding Tangential Acceleration from Radial Acceleration In certain cases, we may need to determine the tangential acceleration from the radial acceleration. Radial acceleration is the component of acceleration directed towards or away from the center of the circle. It is perpendicular to the tangential acceleration. To find the tangential acceleration from radial acceleration, we can use the following formula: – represents the tangential acceleration – is the radial acceleration Calculating Tangential Acceleration from Tangential Velocity In some scenarios, we may need to find the tangential acceleration using the tangential velocity and the time taken to change the velocity. The formula to calculate tangential acceleration in such cases is: – represents the tangential acceleration – is the final tangential velocity – denotes the initial tangential velocity – is the time Determining Tangential Acceleration from Velocity Sometimes, we may need to find the tangential acceleration when only the velocity of the object is known. In such cases, we can use the following formula: – represents the tangential acceleration – is the tangential velocity – denotes the radius How to Find Acceleration Tangential and Normal When an object moves in a circular path, it experiences two types of acceleration: tangential acceleration and radial or centripetal acceleration. tangential acceleration is responsible for the change in the object’s speed or direction along the circular path, while radial acceleration keeps the object moving towards the center of the circle. The sum of these two accelerations gives the total acceleration of the object. How to Find Direction of Tangential Acceleration The direction of tangential acceleration is determined by the change in the object’s velocity along the circular path. It always points tangent to the circular path, either in the same direction as the motion or in the opposite direction, depending on whether the object is accelerating or decelerating. Multivariable Questions on Tangential Acceleration How to Find Tangential Acceleration with Multiple Variables In more complex scenarios, we may come across questions that involve multiple variables to find the tangential acceleration. To solve these problems, we need to carefully analyze the given information, identify the relevant formulas, and apply them step by step. Let’s consider an example: Suppose an object is moving along a circular path with a radius of 5 meters. The object’s tangential velocity is 10 m/s, and the time taken to complete one revolution is 4 seconds. To find the tangential acceleration, we can use the formula: Substituting the given values: Hence, the tangential acceleration is 2.5 m/s². Quick Facts : Q: What is the concept of tangential acceleration? A: The concept of tangential acceleration is related to the acceleration of an object moving in a circular path. It can be understood as the rate of change in the speed of the object along its tangential direction. It is known as tangential acceleration because the direction of the acceleration vector is tangential to the direction of the velocity vector at any given point. Q: What is the formula for tangential acceleration? A: The formula for tangential acceleration is a = r * α, where ‘a’ represents the tangential acceleration, ‘r’ is the radius, and ‘α’ represents the angular acceleration of the object. It is the product of the radius of the motion and the angular acceleration. Q: How does tangential acceleration relate to uniform circular motion? A: In uniform circular motion, the magnitude of the velocity remains constant but the direction of the velocity changes continuously. Hence, there is an additional acceleration acting along the radius towards the center, known as centripetal acceleration. If the object executing circular motion has uniform acceleration, then the tangential acceleration is zero. |Attribute Of Tangential Acceleration |Characteristic in Uniform Circular Motion |None (tangential acceleration is zero) |Not applicable (since speed is constant) |No direction (as there is no tangential acceleration) |0 m/s² (no change in the magnitude of velocity) |Effect on Speed |No effect (speed is constant) |Effect on Trajectory |No effect (trajectory remains circular at constant radius) |Resulting Motion Type |Uniform circular motion (constant speed, constant radius) |No net force in the tangential direction Q: What’s the difference between radial and tangential acceleration? |Radial (Centripetal) Acceleration |Always points radially inward regardless of the object’s motion direction. |Aligned with the instantaneous direction of velocity change, either forward or backward along the path. |Dependence on Velocity |Depends on the square of the tangential velocity (speed) and inversely on the radius of curvature. |Directly related to the rate of change of the object’s speed, irrespective of its path curvature. |Role in Circular Motion |Provides the necessary force component to keep an object in a circular path without influencing the object’s speed. |Responsible for the change in speed of an object in circular motion, without affecting the radius of the path. |Independence from Speed |Independent of changes in the object’s speed; an object in uniform circular motion has constant radial acceleration. |Directly dependent on changes in speed; without a change in speed, tangential acceleration is nonexistent. |Represented in Equations |Prominently features in Newton’s second law for rotational motion (F=ma_r) when considering the force necessary for circular motion. |Featured in the kinematic equations of motion when an object’s speed is changing. |Measured in terms of centripetal force required per unit mass to maintain the circular path (N/kg or m/s²). |Measured as the rate of change of speed, indicating how quickly an object accelerates or decelerates (m/s²). |In Rotational Dynamics |Analogous to force in linear dynamics, but for rotating systems, it represents the radial force per mass needed to maintain rotation. |Analogous to the force component in linear dynamics that causes a change in kinetic energy due to speed variation. |Does no work because the radial acceleration is perpendicular to the displacement of the object in circular motion. |Does work as it is in the direction of displacement, contributing to a change in the kinetic energy of the object. |Effect on Angular Momentum |Does not change the angular momentum of an object in a closed system since there is no torque involved. |Can change the angular momentum if it is associated with a torque, affecting the rotational speed. |Since it doesn’t change the speed, it doesn’t directly contribute to a change in kinetic energy; it affects potential energy in a gravitational field. |Directly affects kinetic energy as it changes the speed; in a gravitational field, it can also affect potential energy. Q: What does tangential acceleration tell us? A: Tangential acceleration gives us an idea about how rapidly the speed of an object is changing with time in the tangential direction. If tangential acceleration is positive, the object is speeding up. If it is negative, the object is slowing down. Q: How does the tangential acceleration formula apply to solving problems? A: The tangential acceleration formula is particularly useful in cases where an object moves in a circular path and its speed changes at a uniform rate. It helps calculate the change in speed at any given point of time. The formula can be applied directly or by integrating the equation if the angular acceleration is not constant. Q: Could you provide a solved example using the tangential acceleration formula? A: Sure. Suppose an object is moving on a circular path of radius 4 meters with an angular acceleration of 2 rad/s². The tangential acceleration (a) would be a = r * α = 4 m * 2 rad/s² = 8 m/s². Here, we’ve used the formula for tangential acceleration to calculate the acceleration of the object. Q: What is the relationship between total acceleration, centripetal and tangential acceleration? A: The total acceleration of an object moving in a circular path is the vector sum of the centripetal and tangential acceleration. Mathematically, total acceleration = √((centripetal acceleration)² + (tangential acceleration)²). The centripetal acceleration is directed towards the center of the circle, whereas the tangential acceleration is in the tangent direction to the circle at that point. Q: How are the tangential acceleration and the velocity vector related? A: The velocity vector of an object executing circular motion has two components: the radial and the tangential. And tangential acceleration has an effect on the magnitude of the velocity vector along the tangential direction. If there is any tangential acceleration, it means that the magnitude of the velocity vector is changing. How can tangential acceleration and angular acceleration be related? To understand the relationship between tangential acceleration and angular acceleration, it is important to consider the concept of Finding Angular Acceleration of a Wheel. Angular acceleration refers to the rate at which the angular velocity of a rotating object changes over time. On the other hand, tangential acceleration refers to the linear acceleration experienced by an object moving in a circular path. These two concepts are interconnected because the tangential acceleration of a point on a rotating object is related to the angular acceleration of the object. By understanding how tangential acceleration and angular acceleration are connected, we can gain insights into the dynamics of rotational motion. Q: What are the applications of tangential acceleration in real life? A: Tangential acceleration has many practical applications in real-life situations such as turning of vehicles where the speed changes due to tangential acceleration. It’s used in the dynamics of rotational motions such as gears, pulleys, and wheels. It’s also applicable in the field of astronomy for studying the planetary motion of celestial objects. - How to find mass and acceleration with force - How to find tension force with acceleration - How to find angular acceleration without time - How to find acceleration projectile motion - Torque and angular acceleration - Centripetal acceleration and mass - How to find acceleration with mass and radius - How to calculate force without acceleration - How to find total acceleration - How to find total acceleration in circular motion Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess.

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https://www.kassonme.new.rschooltoday.com/page/2484

math

GRADE 4: MATH ONLINE ACTIVITIES Unit 1 Learning Goals - NAME/CONSTRUCT GEOMETRIC FIGURES Use a compass and straightedge to construct geometric figures. Identify properties of polygons. Classify quadrangles according to side and angle properties. Name, draw, and label line segments, lines, and rays. Identify and describe right angles, parallel lines, and line segments. Know addition and subtraction facts. Vocabulary Hidden Picture Unit 2 Learning Goals - ORGANIZING DATA Display data with a line plot, bar graph, or tally chart. Use the statistical landmarks median, mode, and range. Use the statistical landmarks maximum and minimum. Subtract multi digit numbers. Add multi digit numbers. Read and write to hundred millions; give values to hundred millions. Find equivalent names for numbers. One False Move Unit 3 Learning Goals - MULTIPLICATION AND DIVISION Solve open sentences. Understand the function and placement of parentheses in number sentences. Determine whether number sentences are true or false. Solve addition and subtraction number stories. Use a map scale to estimate distances. Know division facts. Know multiplication facts. Understand the relationship between multiplication and division. Math Car Racing Unit 4 Learning Goals - DECIMALS Express metric measures with decimals. Convert between metric measures. Read and write decimals to thousandths. Compare and order decimals. Draw and measure line segments to the nearest millimeter. Use personal references to estimate lengths in metric units. Solve 1- 2 digit decimal addition/subtraction and number stories. Draw and measure line segments to the nearest centimeter. Decimal Place Values Unit 5 Learning Goals - ESTIMATION Use exponential notation to represent powers of 10. Know extended multiplication facts. Make magnitude estimates for products or multi digit numbers. Solve multi digit multiplication problems. Round whole numbers to a give place. Read and write numbers to billions; name the values of digits to billions. Compare large numbers. Unit 6 Learning Goals - DIVISION Identify locations on Earth for latitude and longitude. Find latitude and longitude for given locations. Solve whole number division problems. Express remainders as fractions and the answer as a mixed number. Interpret the remainder in division problems. Name and locate points specified by ordered pairs on a coordinate grid. Identify acute, right, obtuse, straight, and reflex angles. Make turns and fractions. What's the Point Find Your Longitude Unit 7 Learning Goals - FRACTIONS Add and subtract fractions. Rename fractions with denominators of 10 and 100 as decimals. Apply basic vocabulary and concepts associated with change events. Compare and order fractions. Find equivalent fractions for given fractions. Identify the whole for fractions. Identify fractional parts of a collections of objects. Identify fractional parts of a region. Fraction Tool Game Fresh Baked Fractions Fractional Sets of Numbers Unit 8 Learning Goals - AREA/PERIMETER Make and interpret scale drawings. Use formulas to find areas of rectangles, parallelograms, and triangles. Find the perimeter of a polygon. Find the area of a figure by counting unit squares. Area of a rectangle Area of a parallelogram Area of a triangle Unit 9 Learning Goals - PERCENTS Use an estimation strategy to divide decimals by whole numbers. Use an estimation strategy to multiply decimals by whole numbers. Find a percent or a fraction of a number. Convert between easy fractions, decimals, and percents. Convert between hundredths-fractions, decimals, and percents. Use a calculator to rename any fraction as a decimal or percent. Unit 10 Learning Goals - REFLECTION/SYMMETRY Use a transparent mirror to draw the reflection of a figure. Identify lines of symmetry, reflection, reflected figures, and figures with symmetry. Fold These Shapes Unit 11 Learning Goals - SOLIDS/WEIGHTS Use a formula to calculate volumes of rectangular prisms. Subtract positive and negative integers. Add positive and negative integers. Estimate weight of objects in ounces/grams, weigh objects in ounces/grams. Solve cube-stacking volume problems. Describe properties of geometric solids. Animal Weigh In Unit 12 Learning Goals - RATES Find unit rates. Calculate unit prices to determine which product in the "better buy". Evaluate reasonableness of rate data. Collect and compare rate data. Use rate tables to solve rate problems.

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CC-MAIN-2023-06

http://web.sonoma.edu/users/w/wilsonst/courses/math_150/hw/3/4-23h.html

math

Use your compass and straightedge and on the triangle below, 1. Construct the perpendicular bisectors of the sides 2. Draw the circumscribed circle. 3. Construct the medians. 4. Construct the altitudes. 5. Find the midpoint of the Euler line. 6. Draw the 9 point circle. 7. Bisect the three angles. 8. Drop a perpendicular from the point where the angle bisectors meet to a side to find a point of tangency. 9. Draw the inscribed circle.

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CC-MAIN-2017-43

http://events.berkeley.edu/index.php/calendar/sn/?event_ID=125531&date=2019-04-29&tab=all_events

math

Differential Geometry Seminar: Non-Archimedean aspects of the space of Kähler metrics Seminar | April 29 | 3:10-4 p.m. | 939 Evans Hall Mattias Jonsson, University of Michigan Let (X,L) be a polarized complex manifold. A good understanding of the space of Kähler metrics in the cohomology class of L is crucial to variational approach to constructing canonical metrics on X. I will discuss joint work with S. Boucksom, in which we analyze geodesic rays in (the completion of) this space, partially from a non-Archimedean point of view.

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CC-MAIN-2019-43

http://www.diysubwoofers.org/bnd/6thord4.htm

math

Order Bandpass Systems Series tuned systems are similar to the 'normal' 6th order bandpass systems, with one major difference - one chamber is vented into another instead of to the outside, as indicated in the diagram below: Calculation of the appropriate length for the inner port is somewhat complex, as both the inner and outer ports work together to tune the rear chamber to a particular frequency. You can simplify the calculations somewhat by using the following method: First, let's choose to use a 4" diameter tube for both vents. To tune a 0.75 cu.ft. enclosure to 100 Hz with a 4" vent, our calculations suggest that the vent will have to be 4.11" long. To tune a 2.25 cu.ft. enclosure to 30 Hz with a 4" vent, our calculations suggest that the vent will have to be 13.76" long. Therefore, if we were to use a 4" tube for the inner vent, it's length will have to be 13.76-4.11 = 9.65" long. Let's say that 9.65" is a bit too long for our needs, so we'd like to use a 3" diameter internal vent instead. First of all, we use the port calculation equations to determine that a 2.25 cu.ft. enclosure with a 4" diameter vent that's 9.65" long will be tuned to 34.6 Hz. Then, using the port calculations, we determine that, to tune a 2.25 cu.ft. enclosure to 34.6 Hz with a 3" diameter vent, the vent will have to be 4.86" long. The physical parameters for our 6th order series-tuned alignment are therefore as follows: Front Volume: 0.75 cu.ft. Note: Typically, to make construction easier, I'd probably want to shift the theoretical resonance frequencies of this alignment up and down just a little, to see if I can get away with 4" and 4.75" instead of 4.11" and 4.86" lengths. Also, the geometry of the front volume may impact Fr as well (pushing it a bit lower, which is usually a good thing!). As with most designs, measure the resonance frequencies after construction, to see how close you've come to the target alignment.

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CC-MAIN-2018-30

https://sciendo.com/fr/article/10.2478/amns.2022.2.0059

math

Because the current computer sensor data positioning analysis has positioning difficulties and false positioning problems, we use the Lagrangian multiplier method of the interactive direction to disassemble the computer sensor sound source. Through this algorithm, the information fusion of computer sensor nodes is realized. After using Lagrangian mathematical equations, these error correction measurements have achieved better target positioning results. Theoretical analysis and experimental results show that the algorithm improves the speed of computer sensor data association. To a certain extent, the correlation accuracy is improved.

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CC-MAIN-2024-10

https://food-le.com/rubik-s-cubicle

math

PUZZLE WORDLEVERSE VARIATIONS brain logic guess rubik If you are a Rubik and logic enthusiast, you can try Rubik's Cubicle. A fun puzzle game about the Rubic cube Logical thinking to solve the Rubik's cube in five moves Not too difficult for those who have played it. Are you the smartest? How to play - The game, invented by Ernő Rubik, consists of a cube that can be rotated on different axes. A large cube face is made up of six small cubes, as you know. Your task is to think and perform rotations using Singmaster Notation, where each letter represents a face. U (up), D (down), L (left), R (right), F (front), and B (back) Make sure the end result is a uniform color on each side. For the sake of clarity, in this cube, F is Blue and R is Orange. - If you see a certain letter, you know you need to spin the object you're viewing clockwise by 90 degrees. If there is a prime mark (′) following the letter, it should be rotated counterclockwise 90 degrees, and if there is a square (2), it should be rotated clockwise 180 degrees.

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https://support.minitab.com/en-us/minitab/21/nav_statistical-modeling-doe-supporting-topics-taguchi-designs/?context=statistical-modeling/doe/supporting-topics/taguchi-designs/what-is-the-signal-to-noise-ratio/

math

Factors in Taguchi designs Steps for conducting a Taguchi designed experiment Notation for Taguchi designs Catalogue of Taguchi designs How Minitab adds a signal factor How to arrange response data Two-step optimization for Taguchi designs Display or change the alias structure How to calculate the signal-to-noise ratios and the standard deviations Interactions and interaction tables What is the signal-to-noise ratio? What is the mean in a Taguchi design? What is the slope? What is the standard deviation? Dummy treatments for Taguchi designs

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CC-MAIN-2023-23

https://ironwildflower.com/improper.nqm

math

The graph can use the difference of identifying polynomial TTL Fund Statements Analyze the transformations of the basic functions. FINDING THE EQUATIONS OF POLYNOMIALS AND OTHER MIXED. For area covered by synthetic division form, keep in mind and finding factors. Then demonstrate that you are correct by writing the polynomial in standard form. Example: Solve each polynomial equation by factoring. Type of worksheets are randomly created and functions. Describe the end behavior of a polynomial function. In standard form, the degree of the first term is the degree of the polynomial. To recap all the skills acquired from the previous handouts and apply them here. Recognize the typical shapes of the graphs of polynomials of degree up to 4. Two Google Forms with links. Unit 2 Review Guide Answer Key. Did you have an idea for improving this content? Which function has more examples of worksheets! Evaluating Polynomials Worksheet Answers Squarespace. To determine its end behavior, look at the leading term of the polynomial function. Press to access the CALCmenu. Factor out the common factor. Polynomials and Polynomial Functions NOTES PACKET. Then, answer each question and justify your reasoning. Use these printable Pre-Algebra Algebra I and Algebra II worksheets to gauge. Bottom of this worksheet has Factor Theorem Quick note and sample problems. The function is not. Algebra 2 Worksheets Polynomial Functions Worksheets. This is a great way to introduce polynomials, Algebra. If you are the site owner, click below to login. Student to graph of polynomials worksheet will help your students the graphs. Identify the Real Zeroes and their Multiplicity Reminder If we have the function. Substitute the given values. ANS: C Group terms.

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CC-MAIN-2022-40

https://www.thestudentroom.co.uk/showthread.php?t=3712029

math

The ends of a long water trough 8ft. long are equilateral triangles whose sides are 2 feet long.? If water is being pumped into the trough at a rate of 5 cubic feet/minute, find the rate at which the water level is rising when the depth is 8 inches. Turn on thread page Beta Can you do this question ? :D watch - Thread Starter - 07-11-2015 11:57 - 07-11-2015 12:13 So let V= volume of water in trough, D= depth of water, t = time (in minutes) dV/dt = 5 (given) V = constant x D^2 (you can work out the constant by finding the area of an equilateral triangle prism with the given dimensions and a height of D) We want to find dD/dt at D=2/3 (since 8 inches = 2/3 feet) So find dV/dD, invert to find dD/dV. Chain rule gives dD/dt = dD/dV x dV/dt then substitute D = 2/3 to find rate of change at a depth of 8 inches...Last edited by Pronged Lily; 07-11-2015 at 12:31. - 07-11-2015 12:34

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https://kbkonnected2.blogspot.com/2015/09/3-halloween-clip-art-collections-to.html

math

I just added these colorful Halloween themed clip art sets. The frames have a fun "shiny" look. Each frame set has 17 frames with 4 versions each. There are 68 png frames in each set. The frame sets are easy to mix and match with the coordinating papers. There are 33 papers in the paper set. Each set is 50% off for the first 48 hours in my TpT store.

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CC-MAIN-2022-21

http://sites.math.northwestern.edu/news/calendar/abstract.cgi?id=1695131975&dyear=2023

math

Title: Vanishing of Brauer classes on K3 surfaces under reduction. Speaker: Salim Tayou Speaker Info: Harvard University Given a Brauer class on a K3 surface over a number field, we prove that there exists infinitely many primes where the reduction of the Brauer class vanishes, under some mild assumptions. This answers a question of Frei--Hassett--Várilly-Alvarado. The proof uses Arakelov intersection theory on GSpin Shimura varieties. If time permits, I will explain some applications to rationality questions. The results in this talk are joint work with Davesh Maulik.Date: Friday, October 20, 2023

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https://math.answers.com/Q/Does_rectangle_have_more_than_one_pair_of_perpendicular_sides

math

No unless it is in the form of a rectangle A rectangle is formed by perpendicular lines that create four 90 degree angles. A square or a rectangle has perpendicular sides that meet each other at right angles which is 90 degrees. The sides perpendicular to each other are at right angles (90 degrees, or square) to each other. An example of a figure with two pair of perpendicular sides is the rectangle. Yes, because if you draw a rectangle, there'll be at the top and the right side touch. The question contradicts itself. A dodecagon need not have any perpendicular sides. A square and a rectangle because their corners meet at 90 degrees shape no pairs of perpendicular sides Any polygon can have only 1 pair of perpendicular sides. I suppose. All of a square's sides are perpendicular. No but its diagonals are perpendicular No not normally

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https://doubtnut.com/question-answer/chakradhar-buys-a-tv-marked-at-rs-14500-after-receiving-successive-discounts-of-15and20-and-paying-1-43959471

math

Chakradhar buys a TV marked at Rs. 14,500 after receiving successive discounts of 15%and20% and paying 10% sales tax. He spends Rs. 2000 on it and sells the TV for Rs. 12,000. Find his gain or loss percent. Question from Class 10 Chapter Taxation Apne doubts clear karein ab Whatsapp par bhi. Try it now.

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CC-MAIN-2020-24

https://apps.dtic.mil/sti/citations/ADA513135

math

Optimality Functions in Stochastic Programming NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF OPERATIONS RESEARCH Pagination or Media Count: Optimality functions in nonlinear programming conveniently measure, in some sense, the distance between a candidate solution and a stationary point. They may also provide guidance towards the development of implementable algorithms. In this paper, we use an optimality function to construct procedures for validation analysis in stochastic programs with nonlinear, possibly nonconvex, expected value functions as both objective and constraint functions. We construct an estimator of the optimality function and examine its consistency, bias, and asymptotic distribution. The estimator leads to confidence intervals for the value of the optimality function at a candidate solution and, hence, provides a quantitative measure of solution quality. We also construct an implementable algorithm for solving smooth stochastic programs based on sample average approximations and the optimality function estimator. Preliminary numerical tests illustrate the proposed algorithm and validation analysis procedures. - Statistics and Probability - Operations Research

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https://forum.bubble.io/t/special-offer-free-cad-mdt-read-description-our-full-inventory-is-going-out-there/135772?page=2

math

My discord is masonpackers_#0001 I would like one for my community! rockhero01#8660 To anybody needing a free CAD still, Hydra Tech offers a free plan that you can create your community with instantly. System: Bismuth CAD - Login/Signup I would like addital infomation about this Vappermox#7315 The free plan is’t that good @Bestgamer323 Why do you say that? @Bestgamer323 We have a feedback center anybody can use. We have 900+ users along with 100+ communities who all say they love the CAD and helped them grow… HT is always looking for additional feedback and if the community believes the free plan deserves more perks than anybody may suggest it. hello could I have a base of mdt please my discord Tainino#3172 thanks ghostXgamer#2796 is my discord I need a cad for my role play server I would like one dillondalton24#6620 Tbh I need one bad, starting a server and struggling. My discord is 失われた#0666

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CC-MAIN-2021-21

https://www.rogerbayerri.com/test/

math

Bulk delete posts If you have a backup of your posts, or you are shure you marked all your posts as SAVE before the infection, you can just erase everything here and import your posts again. 0 posts deleted! (stil 0 to go! if there are no posts showing, probably only save ones left! )

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https://www.chinapostaltracking.com/qa/where-is-my-package-its-stuck-for-44-days-100970/

math

China Post: 86 10 11185 EMS: 86 10 11183 - Q & A Where is my package? Its stuck for 44 days Asked by Princess | My package has been stuck in "handed over to airline? For 44 days already. Where is it? Is it still in china? Will I get my package? Tracking number LY850156869CN You may get the answer from the following articles:

s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030333541.98/warc/CC-MAIN-20220924213650-20220925003650-00171.warc.gz

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https://onlineyukti.com/deriving-a-vertex-form-from-a-standard-form-of-a-quadratic-equation/

math

To change a quadratic equation from a standardized form to a vertex form is quite easy to derive. You can certainly do so if you understand what a perfect square is. In this article, we would show you all the ideal concepts regarding vertex form and vertex formula. Let us start with a technique called “Completing the Square”. Using this technique, we can change a quadratic equation into a perfect square and you would get to know that it can be easily factorized. So, let us check how it is done. Theories regarding a perfect square Let us start with some examples over the application of the technique called “Completing the Square”. The main goal of CTS or Completing the Square is to take any quadratic equation that is not a perfect square and change it into a squared one without even changing the value. We have a few theories regarding this which is listed below. Theory #1: Squares can be easily factorized Any quadratic equation that is a square can be easily factored. Let us take an example: x2 – 16x + 64 is a square which can again be denoted as (x – 8)2. Theory #2: Finding the pattern within squares From the above quadratic equation, we can say that it has a pattern since the leading co-efficient is a perfect square. Thus we can say that squaring half of b is always equivalent to c. So, from the above example we can say that half of b is equal to –(16/2) = -8. Now if we square -8, we get (-8)2 = 64. Theory #3: Retaining the Value Let us take an example of an equation, y=5x – 9. We can add or subtract values in the equation without changing the original value of the equation. For instance, we can add 3 to each part of the equation. Thus we can write, y + 3 = 5x – 9 +3. However, it is not an appropriate purpose to add in this equation, but mathematically, it does not change the value of the equation. Similarly, we can add and subtract the same values from one part of the equation simultaneously. Using the above example, we can say, y = 5x – 9 + 3 – 3. Here we are adding and subtracting 3 within one part of the equation without changing the value of the equation. Finding the vertex and the vertex form Let us take another example of an equation for instance. y = x2 + 8x – 2 This equation cannot be factorized and apparently it is not a perfect square either. As we have said before, to be a perfect square you should square the half of b to get c. But within this equation it is not the same. So, what would be the value of c to make this a perfect square? c should have to be 16 to make the equation a perfect square. Let us add and subtract 16 within one part of the equation. So the equation looks like, y = x2 + 8x + 16 – 2 – 16. Thus, we get a perfect square, x2 + 8x + 16, with some extra values. Let us factor the perfect square and combine the extra values which would lead to: y = (x + 4)2 – 18. This is actually the vertex form of the original equation, y = x2 + 8x – 2 and the vertex is (-4, -18). Thus to summarize, for changing a quadratic equation to vertex form, we need to change it into a perfect square with few extra values. Eventually, we use the half of b and then square it. After that we add and subtracted the squared value within one part of the equation. Lastly, we factorize the perfect square and combine the extra values. For further details regarding vertex formula, book a session with Cuemath for online math classes.

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CC-MAIN-2023-50

https://forums.wolfram.com/mathgroup/archive/1995/May/msg00121.html

math

Re: How fast are Mathematica Versions ? - To: mathgroup at christensen.cybernetics.net - Subject: [mg1150] Re: How fast are Mathematica Versions ? - From: groskyd at gv.ssi1.com (Dave Rosky) - Date: Wed, 17 May 1995 05:49:26 -0400 - Organization: Silicon Systems, Inc. In <3opkp2$7h4 at news0.cybernetics.net>, Roland.Radtke at arbi.informatik.uni-oldenburg.de (Roland Radtke) writes: >Hello! > >I'd like to know how fast different versions of Mathematica >run with respect to each other. I'm interested especially >in data describing how fast these versions are using different >operating systems (preferably referring to PCs). > >Thank you, > >Roland. > > There was a recent article in Byte Magazine (May 1995) regarding Mathematica. There weren't many technical details, but the authors indicated that the recently released OS/2 version of Mathematica ran about 30% faster than the Windows (win32s) version on the same hardware. They also indicated that it was able to handle some difficult cases that would cause the Windows version to crash. There was no comparison made with the NT version. Regards, David (groskyd at gv.ssi1.com) /* Any opinions are my own. */

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https://japanese.stackexchange.com/questions/17765/how-to-express-eternal-endless-love-on-an-engraved-bracelet

math

In a fanfiction i am writing, one of the characters who was born in Japan gives her girlfriend a bracelet she had made, as a sign of her nationality there is an engraving in japanese which, when her girlfriend asks the meaning she replies "It's Nanoha loves Feito Forever" which is actually a reference to when 2 people write their initials in a heart like this ____ ____ / \ / \ / \/ \ / \ \ N T / \ / \ + / \ / \ F T H / \ / \ / \ / \/ N T = Nanoha Takamachi F T H = Fate Testarossa Harlaown (Nanoha says Feito) since i'm a stricter for accuracy with these things i am wondering if this correct? if not what would be the correct way of express what i am trying to achieve

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http://japanese.stackexchange.com/questions/tagged/compounds+syntax

math

Japanese Language Meta to customize your list. more stack exchange communities Start here for a quick overview of the site Detailed answers to any questions you might have Discuss the workings and policies of this site そのようにする + Recognizing a compound そのようにしてこの巨城は、二年の長きにわたってゆっくりと攻略されてきた。 The first thing I had kind of a problem with, is そのようにして... I just have no idea how to translate it. Also, as for 巨城, 巨 doesn't have a prefix form, nor there is ... Jan 28 '13 at 20:21 newest compounds syntax questions feed Hot Network Questions Why is Quicksort described as "in-place" if the sublists take up quite a bit of memory? Surely only something like bubble sort is in-place? How to respond to "Why shouldn't we hire you?" '100' is a magic number Can you cast an instant damage spell between first strike and normal damage? Do's and Don't's of Undergraduate Research Should I add sound effects to my web site? Any issue with nesting "using" statements in c#? move forward and backward by one word For every rational number, does there exist a sequence of irrationals which converges to it? Find a file when you know its checksum? Units conversion : cl to grams What does ImageSize -> 1 -> 1 mean? Tests on more "human-ish" forms Could you please tell me the time? Clad usage - for old dress Proof of combination sum Why do we not shower every night? Why does it say to me that my class does not contain a constructor that takes 0 arguments? X or Y guitarist doesn't know music theory - how true is this statement? Are there any languages or cultures where people speak while inhaling? What's the English equivalent of "Drilling one's head"? If DOS is single-tasking, how was multitasking possible in old version of Windows? Why would spacetime curvature cause gravity? The meaning of く more hot questions Life / Arts Culture / Recreation TeX - LaTeX Unix & Linux Ask Different (Apple) Geographic Information Systems Science Fiction & Fantasy Seasoned Advice (cooking) Personal Finance & Money English Language & Usage Mi Yodeya (Judaism) Cross Validated (stats) Theoretical Computer Science Meta Stack Overflow Stack Overflow Careers site design / logo © 2014 stack exchange inc; user contributions licensed under cc by-sa 3.0

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CC-MAIN-2014-10

https://shibaura.pure.elsevier.com/ja/publications/some-computations-of-frobenius-schur-indicators-of-the-regular-re

math

We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational results, we formulate the theorem of Frobenius for semisimple Hopf algebras and give some partial results on this problem. ASJC Scopus subject areas - 数学 (全般)

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https://eyrieonline.org/5790/features/horizons/new-math-lab-needs-volunteers/?print=true

math

A new “math lab” for students who are struggling with mathematics, similar to the Writing Center, opened April 19 in room 1107 during seminar. The lab should be open every seminar for the rest of the school year and possibly longer. Due to how new the math lab is, several issues are still being worked out. Thornton Thornburg, math teacher and math lab cofounder, plans to “get all the kinks worked out this last quarter” so everything will be ready next year. As of April 26, nine student tutors are working in the math lab. Thornburg and Rachel Jetton, math teacher and the other math lab cofounder, are looking for volunteer tutors. If interested, students can talk to Jetton or Thornburg. There is no solid requirement to meet in order to apply. Instead, Jetton or Thornburg will talk to the student’s math teacher to evaluate whether or not a student is a good fit to volunteer. They are looking for students who have a good grasp in any math field, such as geometry or pre-calculus. Caroline Rodriguez, junior, is a volunteer tutor because she is good at math and likes “meeting new kids and helping them out.”

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CC-MAIN-2021-10

https://discuss.codecademy.com/t/lesson-6-of-javascripting/54041

math

Here is the question Let’s say it’s a full moon tonight, and we want to know what the moon will look like one year from today. We know from the moon phase image to the right that the moon circles the Earth every 27 days, so let’s start by dividing 365 by 27. Here are the instructions lol Now let’s generate a space fact while we learn a brand new operator, called (drum roll please) the modulus. The idea behind the modulus is to show you the remainder after you divide a number. So, if you divide 13 / 5, 5 goes into 13 two times, and there will be 3 remaining. A modulus, denoted by a %, would take 13 % 5 and return the remainder 3. How on Earth is this useful? Let’s ask a question a modulus can solve: What will the moon phase be one year from today

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CC-MAIN-2022-33

https://www.researchgate.net/publication/233439216_Singapore_Review_of_Educational_Events_in_1994_and_1995

math

This chapter provides an overview on simultaneous equation estimation. It is an underlying structure to the coefficient matrix in the linear expected value model, a structure which has proved quite useful to econometric modelers, and review methods of estimating the structural parameters. The chapter describes two-stage and three-stage least squares estimates, k-class estimates, and principal ... [Show full abstract] components estimates. Simultaneous and iterative least squares estimates are considered. The variables, which appear as elements of Y, are called endogenous variables and those which appear as elements of X, are called exogenous variables. A large degree of difficulty in reading the econometric literature on simultaneous equation estimation stems from both (a) the existence of two standard sets of notation, one invented by the Cowles Commission for Research in Economics and one invented by the Econometric Institute of the Netherlands School of Economics, and (b) the different ways of expressing the underlying model, each convenient for a particular derivation or application of a standard estimation procedure.

s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337360.41/warc/CC-MAIN-20221002212623-20221003002623-00166.warc.gz

CC-MAIN-2022-40

http://judaism.stackexchange.com/questions/tagged/etymology+shacharis-morning-prayer

math

Mi Yodeya Meta to customize your list. more stack exchange communities Start here for a quick overview of the site Detailed answers to any questions you might have Discuss the workings and policies of this site Etymology of the word “Vasikin” What is the etymology of the word "Vasikin", used for the Minyan that starts Shemona Esrei at sunrise? Also, is "Vasikin" Hebrew or Aramaic? Jan 11 '12 at 21:13 newest etymology shacharis-morning-prayer questions feed August 2 / 6 Av August 5 / 9 Av Hot Network Questions Will Java Final variables have default values? What should I do if I submitted an article to a predatory journal? How do I constrain variables to a user-defined domain in ArgMax? What is an official collection of laws/books/etc. called? Why does Pluto's orbit cross Neptune's orbit? Show the arrows in a plot Is the Anukramni index of sages and deities of the Rig Veda available online? How does continue work? How do I triangulate a quad the other way? Why are magnetic fields so much weaker than electric? Get SObject by Id Should a progressbar go both ways? Could Khal Drogo's Khalasar really have defeated the Iron Throne? Generally speaking, is it better to make all the functional parts or get UI working first - or a mix of the two? Who is the Main Villain in Hearthstone's Curse of Naxxramas? How can I test out my equipment before a backpacking trip? In quel di Milano Break the popularity contest crypto Where did Machiavelli say that "the ends justify the means"? vim: hide first n letters of all lines in a file Excel VBA program only running at 25% speed Appropriate word for internet name of a person When shorting a stock, do you pay current market price or the best (lowest) available ask price? Ask how to pronounce advisor's last name? more hot questions Life / Arts Culture / Recreation TeX - LaTeX Unix & Linux Ask Different (Apple) Geographic Information Systems Science Fiction & Fantasy Seasoned Advice (cooking) Personal Finance & Money English Language & Usage Mi Yodeya (Judaism) Cross Validated (stats) Theoretical Computer Science Meta Stack Exchange Stack Overflow Careers site design / logo © 2014 stack exchange inc; user contributions licensed under cc by-sa 3.0

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CC-MAIN-2014-23

https://www.ma.tum.de/en/department/news-events/department-colloquium.html

math

The colloquium at the Department of Mathematics takes place in a loose sequence, with two lectures each: from 14:30 - 15:30 and 16:00 - 17:00 in lecture hall 3 (MI 00.06.011). During the break we offer you drinks and pretzels in the Magistrale. Lectures in Winter Semester 2018/19 - 17 Oktober 2018: Claudia Redenbach - 14 November 2018: Michael Dumbser (14:30), Holger Dullin (16:00) - 09 Januar 2019: George Karniadakis & Vlad Vicol - 06 Februar 2019: Thomas Strohmer & Clotilde Fermanian Kammerer 14th November, 14:30 - 15:30 Prof. Michael Dumbser, University of Trento: New mathematical models and numerical algorithms for Newtonian and general relativistic continuum physics In the first part of the talk we present a family of arbitrary high order accurate (ADER) finite volume and discontinous Galerkin finite element schemes for the numerical solution of a new unified first oder symmetric hyperbolic and thermodynamically compatible (SHTC) formulation of Newtonian continuum physics, including a general description of fluid and solid mechanics as well as electro-magnetic fields in one single system of governing partial differential equations (PDE). The model is based on previous work of Godunov, Peshkov and Romenski (so-called GPR model) on symmetric hyperbolic and thermodynamically compatible systems. In the second part of the talk, we show a successful extension of the GPR model to general relativity, leading to a novel and unified first order hyperbolic formulation of general relativistic continuum mechanics. The model is able to describe nonlinear elasto-plastic solids, as well as ideal and non-ideal (viscous) fluids in full general relativity. Formal asymptotic expansion of the governing PDE reveals the structure of the viscous stress tensor in the asymptotic relaxation limit. The key features of the new model are its symmetric hyperbolicity and thermodynamical compatibility. The proposed PDE system is causal, covariant and has bounded signal speeds for all involved processes, including disspative ones. Since the new model also contains elastic solids as a special case, it should be understood as an alternative to existing models for vicous relativistic fluids that are usually derived from kinetic theory and extended irreversible thermodynamics. We present numerical results obtained with high oder ADER schemes for inviscid and viscous relativistic flows obtained in the stiff relaxation limit of the system, as well as results for solid mechanics. In the last part of the talk we introduce a new, provably strongly hyperbolic first order reduction of the CCZ4 formalism of the Einstein field equations of general relativity and its solution with high order ADER discontinuous Galerkin finite element schemes. 14th November, 16:00 - 17:00 Prof. Holger Dullin, University of Sydney: The three body problem in four dimensions The Newtonian three body problem has undergone a Renaissance in recent years. I will present an overview of old and new results on periodic solutions, symbolic dynamics, and chaos in this problem. Then I will describe new results about the symplectic symmetry reduction and dynamics of relative equilibria when the spatial dimension is at least four. In particular we will show that there are families of relative equilibria that are minima of the reduced Hamiltonian, and hence are Lyapunov stable. This establishes the first proof of Lyapunov stable periodic orbits in the three body problem, albeit in dimension four. 17 Oktober, 16:00 - 17:00 Prof. Claudia Redenbach, Universität Kaiserslautern: Anisotropy analysis of spatial point patterns Filippo Santambrogio - Crowd motion and evolution PDE with density constraints Filippo Santambrogio from the University Paris-Sud+TUM/JvN reports on "Crowd motion and evolution PDE with density constraints". Barbara Gentz - Synchronization in the noisy Kuramoto model of oscillators Barbara Gentz of Bielefeld University presents a lecture on "Synchronization in the noisy Kuramoto model of oscillators". Numerical homogenization beyond periodicity and scale separation On January 17th, Daniel Peterseim of the University of Augsburg speaks on the theme "T Numerical homogenization beyond periodicity and scale separation".

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CC-MAIN-2018-51

https://www.nhbs.com/mathematics-of-genome-analysis-book?bkfno=122567

math

The massive research effort known as the Human Genome Project is an attempt to record the sequence of the three trillion nucleotides that make up the human genome and to identify individual genes within this sequence. While the basic effort is of course a biological one, the description and classification of sequences also lend themselves naturally to mathematical and statistical modeling. This short textbook on the mathematics of genome analysis presents a brief description of several ways in which mathematics and statistics are being used in genome analysis and sequencing. It will be of interest not only to students but also to professional mathematicians curious about the subject. Preface; 1. Decomposing DNA; 2. Recomposing DNA; 3. Sequence statistics; 4. Sequence comparison; 5. Spatial structure and dynamics of DNA; Bibliography; Index. '! a suitable textbook for a mathematics course aimed at raising awareness of the challenges that are posed by computational biology. It is also good first reading for mathematics students and professionals who want to get an idea of the exciting mathematical problems in the analysis of biological sequences.' Ralf Bundschuh, Physics Today '! a nice introduction to mathematical and statistical problems in genome analysis ! this text is a highly welcome and valuable enhancement of the existing literature in the field. apart from covering new grounds, the author explains some of the more recent ideas ! with great expertise. the exposition captivates by its systematic clarity, indicated profundity, necessary rigor, and masterly conciseness ! this book will rank among the most important monographs on abelian varieties and theta functions'. Zentralblatt fur Mathematic 'The American Joint Policy Board for Mathematics has chosen the role of mathematics in analysing and understanding the data arising from the Human Genome Project as the theme for Mathematics Awareness Month 2002, . Percus' state of the art snapshot of what is involved in unravelling this 'cunning'st pattern of excelling nature' (Othello, Act 5, Scene 2) could thus hardly be more timely.' The Mathematical Gazette

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CC-MAIN-2023-50

https://www.le-monastierpinmories.fr/science-math/mathematics/142718-mathematics-for-decision-making-calculus-v-2-a-programmed-basic-text-e-wainright-martin-download-fb2.html

math

- Author:E. Wainright Martin - Publisher:Irwin (Richard D.) Inc.,U.S. (December 1969) - FB2 format1230 kb - ePUB format1398 kb - DJVU format1372 kb - Formats:azw docx lit txt Mathematics for decision making. a programmed basic text. by E. Wainright Martin. Published in Homewood, Ill. Calculus, Linear Algebras, Programmed instruction. Mathematics for decision making. Library has: vol. 1. CONTENTS: -. Items related to Mathematics for Decision Making: A Programmed Basic. List this Seller's Books. Mathematics for Decision Making: A Programmed Basic Text (Volume 1, Linear Mathematics). Martin, E. Wainwright Jr. Published by Richard D. Irwin, 1969. Condition: UsedGood Hardcover. From BookDepart (Shepherdstown, WV, . Math Made a Bit Easier: Basic Math Explained in Plain English Larry Zafran . Calculus of Residua: Complex Functions Theory a-2 Leif Mejlbro BookBoon, Published in 2010, 140 pages. Math Made a Bit Easier: Basic Math Explained in Plain English Larry Zafran CreateSpace, Published in 2009, 280 pages. Lie Groups, Physics, and Geometry Robert Gilmore Drexel University, Published in 2007, 222 pages. Mathematical Methods for Economic Theory: a tutorial Martin J. Osborne University of Toronto, Published in 2007, 301 pages. Introduction to Vectors and Tensors Volume 1: Linear and Multilinear Algebra Ray M. Bowen, . C. Wang Springer, Published in 2008, 314 pages. Main Author: Martin, . ainright. Essential business mathematics. by: Snyder, Llewellyn R. Published: (1963). Mathematics for engineering and scientists/ Alan Jeffrey. Elementary linear algebra. Published: Ontario: Richard D. Irwin,Inc. by: Shilds, Paul C. Published: (1968). Mathematics at the University of Trieste; courses of Risk and Insurance, Life in- A. Olivieri, E Introduction . .Can't find what you're looking for? Try pdfdrive:hope to request .Can't find what you're looking for? Try pdfdrive:hope to request a book. Download books for free. Audience: This book will be useful to teachers and undergraduate students of mathematics or finance. Using little high-level mathematics, the author presents the basic methods for evaluating financial options and building financial simulations. Understanding calculus is vital to the creative applications of mathematics in. Understanding calculus is vital to the creative applications of mathematics in numerous areas. This text focuses on the most widely used applications of mathematical methods, including those related to other important fields such as probability and statistics. The four-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. Goalkicker - Programming Notes for Professionals books. Calculus Made Easy - Silvanus P. Thompson (PDF). Mathematics For Computer Science. Programming in Martin-Löf's Type Theory - Bengt Nordstroem Goalkicker - Programming Notes for Professionals books. Category Theory for the Sciences. CK-12 Probability and Statistics - Advanced. Discrete Structures for Computer Science: Counting, Recursion, and Probability - Michiel Smid. Programming in Martin-Löf's Type Theory - Bengt Nordstroem.

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CC-MAIN-2022-27

https://mail.haskell.org/pipermail/haskell-cafe/2011-August/094436.html

math

[Haskell-cafe] Fractional Part cdsmith at gmail.com Wed Aug 3 01:21:14 CEST 2011 On Wed, 2011-08-03 at 02:06 +0300, Ata Jafari wrote: > In the first step I want to write a little code that can give me only > the decimal part of a float. For instance: properFraction from the RealFrac type class will divide into the real and fractional parts. Once you've got the fractional part, converting that into an integer is a bit trickier. First, you should realize that it's only possible if the number has a terminating decimal representation, which happens precisely when it is rational, and in reduced fraction form, the denominator has only 2 and 5 as prime factors. Conveniently, an IEEE floating point number will always be of that form, so if you assume that the implementation uses an IEEE floating point format, you're golden! You'll then want to multiply both the numerator and denominator by a common multiplier to get the number of 2s and 5s in the factorization of the denominator to be the same. Then the denominator is a power of 10, so the numerator is your answer. Some simple code might look like: toDecimalPart x = n * (5^k) where (_, fracPart) = properFraction x r = toRational fracPart d = denominator r n = numerator r k = log2 d log2 1 = 0 log2 n | even n && n > 1 = 1 + log2 (n `quot` 2) | otherwise = error "log2 not an integer" More information about the Haskell-Cafe

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CC-MAIN-2020-34

http://www.physicsforums.com/showpost.php?p=3236647&postcount=1

math

1. The problem statement, all variables and given/known data On the afternoon of January 15, 1919, an unusually warm day in Boston, a 27.4-m-high, 27.4-m-diameter cylindrical metal tank used for storing molasses ruptured. Molasses flooded into the streets in a 9-m-deep stream, killing pedestrians and horses, and knocking down buildings. The molasses had a density of 1600 kg/ m^3 If the tank was full before the accident, what was the total outward force the molasses exerted on its sides? (Hint: Consider the outward force on a circular ring of the tank wall of width dy and at a depth y below the surface. Integrate to find the total outward force. Assume that before the tank ruptured, the pressure at the surface of the molasses was equal to the air pressure outside the tank.) 2. Relevant equations 3. The attempt at a solution if F=PA then dF=dPdA and dA for a cylinder is pi*d (integration of pi*r^2) and for d=27.4, dA=86.1 i have F=86.1*int[101325pascals + (1600kg/m^3)(9.8m/s^2)hdh] from 0 to 27.4 86.1 (101325h+7840h^2) and plugging in 27.4 for h gives 7.46e^8 which is wrong... help?

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http://www.mathisfunforum.com/post.php?tid=19124&qid=258354

math

You are not logged in. Post a reply Topic review (newest first) Find the value of Za* Find z scores that seperate the middle 29% of the distribution from the area in the tails of the standard normal deviation Determine the total area under the standard normal curve

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CC-MAIN-2014-15

http://mathhelpforum.com/pre-calculus/197779-linear-programming-word-problem-system-inequalities.html

math

A hospital dietician wishes. To prepare a corn-squash vegetable dish that will provide at least 3 grams of protein and cost no more that .36 per serving. And ounce of cream corn provides 1/2 gram of protein and costs .04. An ounce of squash supplies 1/4 gram of protein and costs .03. For taste, there must be at least 2 ounces of corn and at least as much squash as corn. It is important to keep the total number of ounces in a serving as small as possible. Find the combination of corrn and squash that will minimize the amount of ingrediants used per serving. I am horrible at word problems and I've been trying to get the hang of it, please help.

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CC-MAIN-2014-52

https://www.physicsforums.com/threads/help-with-thermodynamic-delta.103611/

math

then why can it also equal d( delta G/T)= -delta H/T^2? unless delta=1 then all those things can't be equal. matt,I think that's a thermodynamic relationship. So delta G signifies the change in Gibbs energy between the initial and final states ie, delta G = G_f - G_i The point I was making was that the question is badly written. We shouldn't have to guess what the symbols mean. sorry about that!!! it's a thermodynamics relationship, and i'm confused about why the second equation is right... Separate names with a comma.

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CC-MAIN-2018-13

http://www.mathdemos.org/mathdemos/cycloid-demo/

math

The path of a particle moving in a plane need not trace out the graph of a function, hence we cannot describe the path by expressing y directly in terms of x. An alternate way to describe the path of the particle is to express the coordinates of its points as functions of a third variable using a pair of equations Equations of this form are called parametric equations for x and y, and the unknown t is called a parameter. The parameter t may represent time in some instances, an angle in other situations, or the distance a particle has traveled along the path from a designated starting point. x = f(t), y = g(t). An easy example of a parametric representation of a curve is obtained by using basic trigonometry to obtain parametric equations of a circle of radius 1 centered at the origin. We have the relationships between a point (x,y) on the circle and an angle t as shown in the following figure. By elementary trigonometry we have the parametric As t goes from 0 to 2p the corresponding points trace out the circle in a counter clockwise direction. The following animation illustrates the process. x = cos(t), y = sin(t). (For a related demonstration for generation of sine and cosine curves see the Circular Functions demo. ) Generating a circle based on circles. A famous curve that was named by Galileo in 1599 is called a cycloid. A cycloid is the path traced out by a point on the circumference of a circle as the circle rolls (without slipping) along a straight line. A cycloid can be drawn by a pencil (chalk or marker) attached to a circular lid which is rolled along a ruler. The following animation illustrates the generation of a cycloid. If the circle that is rolled has radius then the parametric equations of the cycloid are x = a(t - sin(t)), y = a(1 - cos(t)) where parameter t is the angle through which the circle was rolled. As in the case of the circle, these parametric equations can be derived using elementary trigonometry. To see the basics of the derivation click on the following: The Equations of a Cycloid. For some history related to cycloids click on the following: St.Andrews-cycloid Take a large circle centered at the origin. Place a smaller circle tangent to the original circle at the point where it crosses the positive x-axis and outside of the original circle. Identify the point of tangency. See the next figure. Next we roll the smaller circle around the larger circle and follow the path of the point of tangency. The resulting curve is called an epicycloid. The shape of the curve generated in this manner depends on the relationship between the radius of the large circle and the small circle. The following animations illustrate three With a careful analysis we can show that the parametric equations of an epicycloid using a large circle of radius and a small circle of radius b, where a > b, are , y=(a+b)sin(t)-bsin((a+b)t/b) . The epicycloid has been studied by such luminaries as Leibniz, Euler, Halley, Newton and the Bernoullis. The epicycloid curve is of special interest to astronomers and the design of cog-wheels with minimum friction. To experiment with epicycloids see the files available at the end of this module. For more information and an on-line animator click on the following link: animator for epicycloid. Here take a large circle centered at the origin. Place a smaller circle tangent to the original circle at the point where it crosses the positive x-axis and inside the original circle. Identify the point of tangency. See the next figure. Roll the smaller circle around the larger circle and follow the path of the point of tangency. The resulting curve is called an hypocycloid. The shape of the curve generated in this manner depends on the relationship between the radius of the large circle and the small circle. The following two animations illustrate the generation of hypocycloids. (Also see the animation at the beginning of this demo.) Again with a careful analysis we can show that the parametric equations of an epicycloid using a large circle of radius a and a small circle of radius b, where a > b, , y=(a-b)sin(t)-bsin((a-b)t/b) . I have used demos of this type in several Each semester for calculus we have four computer labs. Our In calculus class we define parametric equations and have the students plot a few by hand before we do the demonstration. The demonstration then wows them as they realize how difficult it would be to plot these objects by hand. For the epicycloid I usually use two rolls of tape with different radii, identify a point on the outer one with a magic marker, and then roll it around the other and ask the students what they think the path would look like. Then using DERIVE (see downloads available below) we plot epicycloids for various radii and ask questions about what they would expect and (as I already pointed out in discussion) the numbers of times we need to rotate (i.e. what the parameters should be) in order to obtain a closed epicycloid curve. We try to get them to state a little theorem about this. students must go to the lab, perform the exercises or experiments on the computer using DERIVE, and then write up their results. One of these labs requires students to plot a collection of functions using parametric equations and polar coordinates. The main purpose of the lab is to familiarize students with the parametric plotting capabilities of DERIVE. This lab is assigned after students have seen some of the demo material shown above. I have also used this demo or a variation thereof during various admission (student recruiting) days. Generally, here, the audience consists of prospective students and their parents. It is relative easy to explain what the cycloids are and then it is exciting and informative to see them plotted. For DERIVE the following file was supplied by Anthony Berard and can be downloaded by clicking on (See the imbedded instructions concerning change of scale.) For Matlab the following files were written for this demo and can be downloaded by clicking on the file name: epicycloid.m , hypocycloid.m . This demo was submitted by Department of Mathematics and is included in Demos with Positive Impact with his permission.

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https://wohakahyhilitez.maxiwebagadir.com/facing-math-lesson-11-writing-and-evaluating-expressions-in-math-53293kd.html

math

All my subtraction words will be another color, etc. How many fives are in the model. And, I'm definitely using a ruler next time I draw a table. What should students know and be able to do as a result of this lesson. Make sure that they get the following clue words on the chart paper, along with the operation they indicate, and any more that you or they can think of All of these features are available for anyone to try out by simply selecting a lesson below. This game will help us practice finding clues to help us understand the meaning of different expressions. Still need to tackle my classroom management plan and syllabi. What expression could we write to represent the model. Jensen likes to divide her class into groups of 2. PARCC Algebra 1 test prep books and practice questions are not enough, and classes and tutors are too expensive. Here are a few examples: In 5th grade and in Module 2 of this year, you have used similar reasoning to solve problems. This triggers yesterdays discussion about representing multiplication when there is a variable. In the problem above, the variable g represents the number of groups in Ms. Make sure you are circulating actively, going to each group multiple times, making sure that they are making the connection between the expression and the written phrase they are creating. Examples of Algebraic Expressions An algebraic expression consists of numbers, variables, and operations. Grade reporting and progress tracking We offer detailed grade reporting and progress tracking to keep on task while completing your SAT Math prep course. It's seriously pretty sad looking. An Algebraic expression is an expression that you will see most often once you start Algebra. I like"underline unit vocab with yellow" as one CWP. How many a's are in the model. The lessons are very informative and easily understandable. The value of this number can change. If you make a mistake, choose a different button. You and your partners should be talking about the clues that you can find, before you write the algebraic expression. What are terms associated with the four operations. I got 6 to fit to a page. How did you know what the constant was. Remember, you will have to be a detective and look for math clues to change "math talk" into English and English into "math talk". I circulate around the room and add challenges and supports as needed. The students will write 4 - c when the correct answer should be c - 4. Copyright © by Holt, Rinehart and Winston. 68 Holt Mathematics All rights reserved. Simplifying Algebraic Expressions LESSON Copyright © by Holt. FACEing Algebra Book. You may order this book online TODAY!!! Lesson 1. Solving One-Step Equations using Addition and Subtraction. Lesson 2. Solving One-Step Equations using Multiplication and Division. Lesson 3. Lesson Solving One-Step Inequalities using +, - x, and ÷. Common Core Grade 7 Math (Worksheets, Homework, Lesson Plans) Related Topics: Common Core Math Resources, Lesson Plans, & Worksheets Common Core Math Video Lessons, Math Worksheets and Games for Grade 7 Lesson 18, Worksheets, Lesson 19, Worksheets: Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers. writing during a math lesson is more than just a way to document information; it is a way to deepen student learning and a tool for helping students gain new perspectives. We have learned that, in in an algebraic expression, letters can stand for numbers. When we substitute a specific value for each variable, and then perform the operations, it's called evaluating the expression. Let's evaluate the expression 3y + 2y when 5 = y. Module Overview NYS COMMON CORE MATHEMATICS CURRICULUM 7•2 maxiwebagadir.comA.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 2 Use properties of operations to generate equivalent expressions. maxiwebagadir.comA.2 3. Understand that rewriting an expression in different forms in a problem context can shed light.Facing math lesson 11 writing and evaluating expressions in math

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CC-MAIN-2021-49

http://wingle.jp/some-infinities-are-bigger-than-other-infinities.html

math

Question 1: How many non-negative integers are there? In other words, p is a real number without a natural number partner—an apple without an orange. The tl;dr version is: Assume the numbers between 0 and 1 not including 1 itself are countable aleph-zero cardinality then you can order them 1, 2, 3, 4. I then took out my clothes as I put them in my backpack before I shifted into my Grey Wolf. When you receive the information, if you think any of it is wrong or out of date, you can ask us to change or delete it for you. The weird thing is that it seems like this definition should be obvious that no matter how many things there are, of course you can list all of them. I suppose this is largely a matter of taste. So they're the same size. He is the soon to be Alpha of the Dark Shadows Pack. The natural numbers look nothing like the rational numbers, but both are countably infinite, for example. Coly walked over to me as we gave a wolf hug, I'm sorry it has to be like this, I don't think Aaron realises what he is doing by sending his mate off to be a rogue I know what you are thinking, How does he know? I was walking around taking a breather as I realized how dehydrated I really was. We've gone beyond aleph null. Then you know that the set of men in the room is the same size as the set of women there. It is continuous and flowing, never sharp, never pointy. Can we arrange this into a countable list? This is the first counter intuitive point of infinite numbers. It's kind of independent of standard axioms. This entry was posted in on by. Hazel and Augustus are both smart, thoughtful kids who are coping with terrible circumstances, but they also have that combination of naivet? The most common challenge to mathematical platonism argues that mathematical platonism requires an impenetrable metaphysical gap between mathematical entities and human beings. The basic idea is to assume that you have such an association and then construct a number between 0 and 1 that isn't associated to any integer. Let's say it starts like this: 1 0,1,1,0,1,0,. Let's call the number of positive integers Aleph Zero, because that's what it's called. So it therefore cannot be on the list. Even after a sustained effort lasting more than half a century, no renormalized quantum field theory of gravity has ever been produced. The question is, is there a function that maps every real number or even just the real numbers between zero and one to a unique counting number and vice versa. It means first of all that gravity is infinite at the center of a black hole. Zero is one of the original stumpers. Certainly we can say that some infinite sets are bigger than others, as mathematics nowadays routinely does. Same thing with time: will it go on for all eternity, and does it stretch back infinitely far into the past? After even more torture with the Red Moon Pack, I finally escape to stumble stupidly across another pack territory. Furthermore, if S is a set, then the power set of S always has cardinality strictly greater than that of S, so there cannot be a largest cardinal number. Pick any ordering, write out the numbers in their decimal expansions, then from the first number, take the first digit after the decimal point, second number pick second digit after the decimal point, etc. But what does Aleph Zero + Aleph Zero equal? I hope it is clear, my english is not that good. But we can also say that the set of numbers is only finite, as I have suggested there would be some rationale for doing. Unified field theory Excerpt: Gravity has yet to be successfully included in a theory of everything. What we do know is that if life has infinite moments or infinite love or infinite being then a life twice as long still has exactly the same amount. Edit: If the columns of this matrix : consist of the digits of each number in my list and the rows for each number, what number is not in my list? If you take the numbers in the diagonal in a sequence, and then invert them, the sequence formed will never be found in the set. Now ask, are there more natural numbers than even numbers? Specifically, the fact that Jesus Christ dealt with both general relativity and quantum mechanics in His resurrection from the dead is made evident by the Shroud of Turin. And in fact, with one crucial qualification that we shall come back to, this argument can be applied to anything whatsoever: there are more sets of bananas than there are bananas, more sets of stars than there are stars, more sets of points in space than there are points in space, more sets of sets of bananas than there are sets of bananas, and so on. As soon as we cross the territory boundry line. How many permutations can this number have? You can't find any number that I haven't used. Why can't X exist on the list somewhere else? He did this by contradiction, logically: He assumes that these infinite sets are the same size, then follows a series of logical steps to find a flaw that undermines that assumption. We have no control over, and assume no responsibility for, the conduct, practices or privacy policies of MailChimp. Going all the way to Aleph Zero, you are still limiting your set, essentially, to an identity matrix sort of number: with 1's only at ii, and with the rest of the row being 0's. This is the whole point behind reductio ad absurdum arguments - you follow logical steps and if you come to a contradiction an absurd claim then you know your initial assumption was wrong. A non renormalizable theory has no predictive value because it contains an infinite number of singular coefficients. And what does that mean? The proof of this is known as. Thus you know that the set of older twins that have ever been born is the same size as the set of younger twins that have ever been born. This is true, there is a contradiction here. For instance, the set of real numbers is larger than the set of integers. If the previous statement, some infinities are larger than others is true then we can also say some infinities are smaller than others and also some infinities are equal in size to others. What the two theories have in common — and what they clash over — is zero. Of supplemental note is this quote from Newton: The Supreme God is a Being eternal, infinite, absolutely perfect;,,, from his true dominion it follows that the true God is a living, intelligent, and powerful Being; and, from his other perfections, that he is supreme, or most perfect. We have taken reasonable measures to protect information about you from loss, theft, misuse or unauthorised access, disclosure, alteration and destruction. If I'm incorrectly paraphrasing you, correct me. How can there be more sets of anything than there are sets altogether? We use MailChimp to issue our newsletters, donation requests and reader surveys. He is not eternity or infinity, but eternal and infinite; he is not duration or space, but he endures and is present. I can post it myself, but probably not until later.

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CC-MAIN-2021-17

http://heli-air.net/2016/02/11/the-kutta-joukouski-theorem/

math

The Kutta-Joukouski Theorem It is shown in Section 4.7 that an integration of the pressure distribution on a lifting cylinder leads to the result that the lift per unit span is proportional to the circulation around that cylinder. The Kutta-Joukouski Theorem states that for any body of arbitrary cross section (e. g., an airfoil), the lift per unit span L’ = рУмГ, where Г is taken around any closed path enclosing the body. The proof of the theorem is beyond the scope of this book. However, the theorem was demonstrated to be true for a right circular cylinder by integration of the static pressure acting on the surface of a body, and it is shown later to be true for an airfoil shape. The importance of this theorem is that it provides an alternative way to calculate the lift force on a lifting body. Instead of calculating the velocity magnitude at a point on the body surface, then using the Bernoulli Equation to evaluate the pressure there, and finally integrating to determine the force, the theorem states that the lift force can be found simply by calculating the circulation around the body. As previously mentioned, it often is easier to calculate the circulation than it is to determine the pressure distribution. Of course, if the pressure magnitude at a point or the pressure distribution on the body surface is required, the theorem is of no help because it speaks only of the net force. This theorem is the basis for the so-called circulation theory of lift. This is a mathematical method of calculating lift that convenient for many inviscid-flow problems. However, remember that the lift (and drag) on a body is physically generated by the pressure (and shear-stress) distribution over the surface. The oncoming flow adjusts to accommodate the presence of the lifting body and, in so doing, sets up a velocity and pressure field such that the circulation around the lifting body is nonzero. To fix ideas regarding lift and circulation, imagine a two-dimensional wing installed at an angle of attack in a wind tunnel. Also imagine that there is a suitable instrument available that measures the flow velocity (i. e., magnitude and direction) at numerous points around the wing. The particular points of interest are located along a closed path in a vertical plane aligned with the oncoming stream. Make the measurement, form the vector-dot product V • ds at each measurement station, and sum around the closed path. This calculation of circulation yields a positive quantity that is equal to L7pVTO. Thus, the lift (i. e., physically, the net pressure force acting upward on the wing) is exhibited as a circulation around the wing. Recall an analogy in Chapter 3 in which a measurement of drag was carried out by evaluating the momentum loss in the wake. There, the drag was due physically to the pressure and shear forces acting on the body surface and the drag was exhibited as a momentum loss. Remember that the presence of a circulation around a body does not imply any fluid particles rotating about it. It simply means that the flow above and below the lifting body is higher and lower average velocities than the zero-lift value, respectively.

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CC-MAIN-2021-39

https://www.easternregiontraining.co.uk/course/vocational-training/edexcel-functional-skills-maths/

math

- Representing using mathematics - Analysing situations mathematically - Interpreting solutions to problems using mathematics - Coverage of mathematical content in number, geometry and statistics. Candidates are assessed throughout the course through written and video evidence as well as exam results. 8 Days + External Learning This course enables progression onto further education.

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CC-MAIN-2019-30

http://umj-old.imath.kiev.ua/article/?lang=en&article=9387

math

A Problem with Condition Containing an Integral Term for a Parabolic-Hyperbolic Equation In a layer obtained as the Cartesian product of an interval $[−T_1 ,T_2], T_1 ,T_2 > 0$, and a space $ℝ_p, p ≥ 1$, we study a problem with nonlocal condition in the time variable containing an integral term for a mixed parabolic-hyperbolic equation in the class of functions almost periodic in the space variables. For this problem, we establish a criterion of uniqueness and sufficient conditions for the existence of solutions. To solve the problem of small denominators encountered in the construction of the solution, we use the metric approach. English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 5, pp 723-734. Citation Example: Kuz A. M., Ptashnik B. I. A Problem with Condition Containing an Integral Term for a Parabolic-Hyperbolic Equation // Ukr. Mat. Zh. - 2015. - 67, № 5. - pp. 635-644.

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CC-MAIN-2021-04

http://physicscentral.com/buzz/blog/index.cfm?postid=7012701204663893310

math

Correction: Does 1+2+3+4+ . . . =-1/12? Absolutely Not! (I think) (If you'd rather just know what 1+2+3+4+ . . .actually is equal to, check out our next post in this series) Brief Summary: 1+2+3+4+ . . . is not equal to -1/12, but both the infinite series and the negative number are associated with each other in a way that can be seen in this graph The area of the little region below the horizontal axis equals -1/12, and the infinite area under the curve on the right gives you 1+2+3+4+. . . , which goes to infinity as you add terms, not to -1/12. (Update 2-6-14: of course, this graph shows what it looks like if you can only see a finite region of the graph. So 1+2+3+4+...+m is going to infinity, provided m is some finite number. This doesn't say anything about what happens if you could see all the way to infinity - I'd need a much bigger screen for that. For this reason, I am crossing out all the things that I am not so sure about in this post.) For a longer explanation, read on . . . Thanks in large part to the patience and persistence of people like Bernd Jantzen, who commented extensively on my previous post on this subject, I have found a way to simply, and graphically explain how the series 1+2+3+4+ . . . is associated with (and not equal to) the number -1/12, (update 2-6-14: provided you are actually taking the limit as you add terms and not looking at all the infinite terms at the same time as the Numberphiles did). I usually try to avoid writing equations on this blog, so you're going to have to bear with me. But at least there will be pictures, and those are the most important parts. Here we go . . . I find it easier to understand things visually, so it occurred to me to plot out the series 1+2+3+4+ . . . at various points as you add the numbers. These points are called partial sums. This is what you get if you stop the sum after each step for n=1 the partial sum is 1 for n=2 the partial sum is 1+2 = 3 for n=3 the partial sum is 1+2+3=6 for n=4 the partial sum is 1+2+3+4=10 for n=5 the partial sum is 1+2+3+4+5=15 If you draw the first five terms on a piece of paper, it looks like this But you don't have to add all those numbers to calculate value at each point. The numbers, it so happens, are a sequence (1,3,6,10,15, . . .) that you can calculate with a simple formula called a generating function. In this case the generating function is To get a number at any point in the sequence, like say the 5th spot, just plug in 5 for n, and you get the answer for n=5, G(5)=5(5+1)/2=15 As it turns out, you can also use the generating function to figure out what the values would be between whole numbers. Essentially, you replace the number n with an x, which can have any numerical value you like. If you plot the result, you get this, for positive x. The curve you see here goes up to infinity as x goes to infinity. So far, so good. But if we're going to plot the graph between the various values of n, we might as well look at negative values of x too. When you do that, you get a graph like this There are three interesting areas in this graph. The area above the horizontal axis and to the right of the curve (let's call it A), the area above the horizontal axis and to the left of the curve (call it B), and the area trapped between the curve and the horizontal axis (which I call C). A and B are large areas - infinite actually, as you extend the curves to infinity, but C is small. In fact, if you use calculus to determine it's size, it's 1/12. And because it's below the axis, it's conventionally considered negative, so it's -1/12. It's an easy integral to do, but in case you're feeling lazy, I did it on Wolfram Alpha for you, just click here. Interesting, isn't it? The curve generated using the partial values of the series 1+2+3+4+ . . . gives you a graph with a little region in it that has an area of -1/12. Hmmmmm. This is how 1+2+3+4+ . . . and -1/12 are associated. They aren't equal (update 2-6-14: provided you are taking limits), but -1/12, in the form of area C, is a characteristic of the curve While 1+2+3+4+ . . is the series that generates the curve in the first place. So, despite my previous, non-mathematical argument to the contrary . . . Update 2-6-14: The limit as m goes to infinity of 1+2+3+4+ . . .+m does not equal -1/12. As I see it, -1/12 is a kind of label for the curve that you can generate using partial sums of 1+2+3+4+ . . . The same thing works for 1+2^3+3^3+4^3+ . . . , and 1+2^5+3^5+4^5+ . . . and so on for any odd power (i.e., zeta(-3), zeta (-5), etc). I used this method to calculate the associated values of the zeta function for powers up to 13. In each case, you get a specific value the area C that's associated with the zeta function that creates the curve. Here's a list of the C areas I calculated for curves generated by several series zeta(-1) = 1+2+3+4+ . . . ---> -1/12 zeta(-3) =1+2^3+3^3+4^3+ . . . ---> 1/120 zeta(-5) =1+2^5+^5+4^5+ . . . ---> -1/252 zeta(-7) =1+2^7+3^7+4^7+ . . . ---> 1/240 zeta(-9) =1+2^9+3^9+4^9+ . . . ---> -1/132 zeta(-11) =1+2^11+3^11+4^11+ . . . ---> 691/32760 zeta(-13) =1+2^13+3^13+4^13+ . . . ---> -1/12 They agree with the published values of the zeta function for negative integers listed on Wikipedia. (Although Wikipedia stops at zeta(-7) and I go to zeta(-13). The fact that the number associated with zeta(-1) and zeta(-13) are the same looks like potential trouble, BTW - after all, how would you know if your -1/12 is associated with zeta(-1) or zeta(-13)? It also suggests that the Numberphiles could have shown that -1/12 = 1+2^13+3^13+4^13+ . . ., or that 1+2^13+3^13+4^13+ . . .= 1+2+3+4+ . . ., if they felt like it.) This little procedure works for even powers too, except the answer is always zero. Here's what the C area looks for for the curve generated from zeta(-2)=1+2^2+3^2+4^2+ . . . The parts above and below the axis cancel for all series of this type with even powers, and as a result the total area doesn't give you any information. As you can see for the integral of the curve that comes from1+2^2+3^2+4^2+ . . . How Could I Have Screwed Up So Badly? I'm going to blame my misadventure on the trouble with using words to describe mathematical ideas. Before working out this problem, there was no way I could understand what it means when someone says that the value of -1/12 "can be assigned to an infinite series." They sounded like gibberish, Ramanujan is to blame a bit too. After all, how are we supposed to understand what he was trying to say here? "I told him that the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 + · · · = −1/12 under my theory. If I tell you this you will at once point out to me the lunatic asylum as my goal." -S. Ramanujan in a letter to G.H. Hardy Are we supposed to realize that "under my theory" means that "=" doesn't mean equal? I haven't found his original work, but several people have reproduced a calculation by Euler that uses an equal sign in the same way. If the two sides aren't equal then, as I recall from second grade math, you can't use an equal sign. At least one person I spoke to said that in order to understand it, you have to know what the ". . ." in the expression 1+2+3+4+. . . means. As you can see from the example above, the dots mean exactly what they always mean. If they didn't, then we'd be in almost as much trouble as having equal signs that don't mean equal. Finally, there are the physicists that say they need the relation 1+2+3+4+ . . . = -1/12. Some of them seem to believe the equation is what it is, and that our failure to understand it shouldn't stand in the way of using it. That struck me as the most romantic view, and it was the one I latched onto at the end of the day. Now, I realize that this is a far too mysterious view. It's interesting, but I hope this post shows While 1+2+3+4+ . . . = -1/12 is clearly not true I hope there are other, comparably bizarre mathematical controversies out there. One thing is for sure, though, I'm not going to rely on words, even from the most decorated experts in their fields, to try to understand things like this. I'm going to get out a pencil, fire up Wolfram Alpha, and just do the math. Andy Holland said... In order to use negative numbers for the integral, doesn't that require the problem to be the sum of all natural numbers including the negative ones? The left hand integral area cannot cancel the right hand area otherwise. The sum of all natural numbers from -x to x in the limit as x approaches infinity is -1/12? Monday, July 18, 2016 at 10:44 PM alan doak said... Every term of Zeta(-1) is larger than Zeta(1), except the first which are both 1. Since Zeta(1) equals infinity (proven by the comparison test) -> Zeta(-1) is also infinity, due to the comparison test. QED. Thursday, June 23, 2016 at 9:38 PM Ronnie Johansson said... Please delete "Dr Ebute"'s fraudish nonsense. Tuesday, May 3, 2016 at 6:05 AM Merychris Calib-og said... How can I find the following cardinalities? Sunday, January 31, 2016 at 7:29 AM The term above -143n^10 should be -143n^10/60. Inadvertently the denominator 60 was omitted.Also the term n^c should be +n^c with a plus sign inserted. Integrating this corrected function from 0 to -1 will now render the result of -1/12 = RZ(-13) = RZ(-1). Alan Walter,Sydney. Friday, January 29, 2016 at 9:00 PM Thanks for your youtube email reference. RZ(-c) is Riemann's Zeta value at -c = I(n=0to -1)[1^c+2^c+3^c+...+n^c]dn Where I(n=0to-1) is the definite integral from 0 to -1(lower limit) RZ(-13)=I(n=0to-1)[1^13 +2^13 +3^13 +...+n^13]dn +715n^4/132 -691n^2/420]dn= -1/12 on evaluation= -B(14)/14= -(7/6)(1/14) Note1^c+2^c+3^c+...n^c for odd c values has factors of n(n+1)with zeros at 0,-1. Anyone interested in an expression for the yet unsolved sum of the positive ODD Zeta series Z(2n+1) in terms of π^(2n+1)? Alan Walter, Sydney. Wednesday, January 27, 2016 at 8:39 PM The author of this article is absolutely correct to point out that these supposedly mysterious values can be found by calculating the definite integral between 0 and -1 of the expression for the respective sum to the nth term (a.k.a. their partial sum expressions). This is also mentioned in this interesting 'response' video (it responds to the claims made in the video that is the subject of this discussion): https://www.youtube.com/watch?v=BpfY8m2VLtc It shows what happens if you do the series manipulations with rigorously (hint - you do not get -1/12) and it explains why other methods get this -1/12 result. The response video claims this -1/12 result is the result of a mistake. The mistake is one of taking a function that applies to just positive whole numbers, manipulating it in ways that bring decimal numbers and negative numbers into play, and then interpreting the result as though it still relates to positive whole numbers. Tuesday, January 26, 2016 at 7:02 PM Let's assume I gave you zero fucks. How many fucks have I given you? Friday, May 15, 2015 at 11:28 PM Interesting, except removing thingZ from bagA doesn't leave you with -thingZ in bagA. to do that you would have to remove 2*thingZ. Otherwise, taking thingZ out of bagA, and then replacing it would leave you with nothing in bagA. But clearly removing thingZ from bagA and replacing it shouldn't make thingZ dissappear. Friday, April 3, 2015 at 9:39 AM I understand how puzzling it can be. Is zero a quantity or not? Is a negative number a quantity or not? Talking about apples and pears is a little worn out, I think. There are two different bags; let's call them bagA and bagB. They are freshly made, and nothing has ever been put in them before. Each bag has nothing in it. The bags are in an enclosed vacuum, so there is no air in them and no air outside of them. There are two different things; let's call them thingZ and thingY. You put thingZ into bagA, and thingY into bagB. You then have a bag - bagA - containing thingZ and a bag - bagB - containing thingY. If you remove thingZ from bagA and thingY from bagB, the bags will then be empty because the things that were in them have been removed. Because there used to be a thingZ in bagA, and one was taken out, there is a shortage of one thingZ. BagA therefore contains -1 thingZ. Likewise, bagB therefore contains -1 thingY. But all the time there was a thingZ in bagA, bagA also had no thingY. Similarly, while there was a thingY in bagB, bagB also had no thingZ. In fact, ever since the bags were made, there was also none of thingX, none of thingW, no tomatoes, onions, apples, bicycles, orang-utans or saxophones in them. None of any other thing, in fact, in either bag. And the same goes for what is outside of each bag either, because it was a vacuum. If it is true that zero is something that does exist, then zero is a complete lack of stuff. But we know that it wasn't always like that, because there used to be a thingZ and thingY in the bags. Regarding anything and everything else, there always was a complete lack of anything else in the bags, and everything outside the bags. Because you cannot remove something that isn't there, bagA still contains zero thingY and bagB still contains zero thingZ - and zero everything else except as was stated in the paragraph before this one. And outside of the bags is still zero everything. But the bags don't contain zero of everything, they contain -1 of one thing. Zero is more than -1. The bags therefore collapse under the pressure of absolutely nothing. Friday, April 3, 2015 at 2:30 AM do you wants....idea from amateur...from me or not... Easy...! Open Mind... Zeta Functions not importtant ....Harmonic important more! Zeta function that important Zeta(-1) and Zeta(-3) I show you....develop zeta in term cartoon.....and blinding set and anti and i predict somethings in Higher Dimension...You can help me proof Wednesday, December 3, 2014 at 11:13 PM To be more specific, irrational mathematics('mathematics'), is not sustainable. Monday, November 3, 2014 at 11:53 PM I have posted a message explaining the dilemma. What has happened here was inevitable, mathematics is not sustainable. Here is the link to my message: http://marques.co.za/duke/news_win.htm It will not surprise me if this comment is censored (Moderated) Friday, October 31, 2014 at 5:13 AM 1+2+3+4+... = -1/12 (R) where (R) is the Rumanujan Summation. This is not a normal -1/12. It basically is a categorization of the series in question. It should be read, "the sum of one plus two plus . . . has a Rumanujan summantion of -1/12" (as opposed to "equals -1/12"). Tuesday, October 14, 2014 at 3:12 PM Johnson Briney said... Contact a Great man on [email protected] or call him on +2347060552255 who help me to solve my problems when my ex boyfriend was blackmailing me after trying many ways to stop him but it didn't work for me until i met this man who help me cast a spell that stop him for blackmailing me and now he is pleading forgiveness and i believe he can solve any problems you are having because he just solve mine. Sunday, August 31, 2014 at 9:38 AM way2 college said... Valuable liveliness is also saved which you can set aside to your family or to manually. Completing an Online Distance Learning course gives you more flexibility while studying over conformist classroom set up. Saturday, August 9, 2014 at 1:31 AM No, zero is not in the real world. Imagine that you have two bags, in one there is one apple and in the other you have one pear. Then we remove the apple and the pear out of the bags, now in one bag you have zero apples and in the other zero pears, but zero apples and zero pears have the very same properties, therefore they must be the same thing, as we know, pears and apples are not equal to each other, so it must be that zero is nothing but a concept that does not exist in the real world. Monday, June 2, 2014 at 1:58 AM Area A = Area B since they both are infinitely large areas. That series diverges, you learned that in Cal2 or Math Physics of DiffEq. C'mon. Thursday, May 29, 2014 at 10:47 AM Richard Smart said... This article is superb, I love it. That infinite series thing really perturbed me when I first saw it but I couldn't see how to examine it more effectively such that I could get to the point that I wasn't perturbed by it any more. Watching you do it above now makes me annoyed I didn't have the idea of doing that myself. But the fact is I didn't. So simple, so insightful, so satisfying. Thanks for that and if you could now just solve every other annoying problem for me I would be most grateful ;o) Thursday, May 22, 2014 at 3:41 PM Bernd Jantzen said... Of course, the partial sums of 1+2+3+4+... are tending to infinity. Nobody claimed anything different. The whole discussion here is about how to assign a meaningful finite value even to a divergent sum like this one. And the discussion is about the question whether one may call this finite number the value of the divergent series or just a meaningful number that one may use in replacement of the series under some conditions. Sunday, April 6, 2014 at 6:01 PM Saturday, April 5, 2014 at 10:22 AM Saturday, April 5, 2014 at 10:20 AM i think 1+2+3+4+.........=infinity Saturday, April 5, 2014 at 10:18 AM I possess no sheep, therefore I possess 0 sheep. 0 is very much in the real world. Wednesday, March 19, 2014 at 11:08 AM Imre Fabian said... For me, not a mathematician, this is a perfect example for that you can prove anything with infinity mathematics. In my view, infinity does not exist (in the real world), nor does 0. Infinity = anything / 0 0 = anything / infinity. Physical argument: the smallest thing (measure) is the planck dimension (planck lenght, planck time etc.) so there cannot be an infinite number of since the beginning of time (the big bang). Wednesday, March 5, 2014 at 4:58 AM

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https://oassignment.com/product/qnt-561-week-3-team-assignment-superfun-toys-case-study/

math

QNT 561 Week 3 Team Assignment, SuperFun Toys Case Study SuperFun Toys has decided for the 2018 holiday season to sell a new talking teddy bear called Weather Teddy. This has a built-in barometer that selects one of five responses predicting the weather when a child presses the bear’s hand. Management has recommended ordering quantities of 15,000, 18,000, 24,000 or 28,000 units. This illustrates a lack of consensus of market demand. Team will use the forecaster’s prediction to describe a normal probability distribution to approximate the demand distribution, will sketch the distribution to show its mean and standard deviation, will compute the probability of a stock-out for the order quantities (15,000; 18000; 24,000; 28000), and compute the projected profit for the order quantities……..

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https://bigsurspiritgarden.com/2022/12/15/how-do-you-find-the-frequency-reuse-factor/

math

How do you find the frequency reuse factor? The number of cells after which a frequency channel can be reused is called as the Frequency reuse factor (R.F). It is given by R. F=1/N, Where N is the cluster size. What do you mean by frequency reuse factor? The frequency reuse factor is defined as 1 over the number of cells in the cluster of the system. Valid clusters are those that result in 6 cells with the same frequency of a particular cell located at equal distance from it. What is the frequency of reuse? Explanation: Frequency reuse is the process of using the same radio frequencies on radio transmitter sites within a geographic area. They are separated by sufficient distance to cause minimal interference with each other. 5. What is the frequency reuse factor in CDMA? Figure 1.10 shows how CDMA systems can reuse the same frequency in each cell site. This example shows that the frequency use factor is 1 (N=1) and that the overlap of the radio channels results in an increased interference level in the overlapping area. What is I and J in frequency reuse? Cluster patterns and the corresponding frequencies are re-used in a regular pattern over the entire service area. Frequency reuse plan for C = 3, with hexagonal cells. ( i=1, j =1) Frequency reuse plan for C = 7 (i=2, j =1). The total bandwidth for the system is C times the bandwidth occupied by a single cell. What will be the co-channel reuse ratio of frequency reuse factor N is 12? N. Using equation (2.3), the next possible value of N is 12, (i= j = 2). The corresponding co-channel ratio is given by equation (2.4) as D/R = 6.0. Which is better a low reuse factor or a high reuse factor? Answer. Answer: The lowest reuse factor (K = 1) maximizes capacity; but this has to be balanced with interference considerations: indeed a higher reuse factor (K = 3, 4, 7, or higher) provides more distance between cells using the same frequency, which lowers interferences. What is co-channel reuse ratio? The channel reuse ratio in a cellular system is defined as the ratio of the distance between cells using related channels to the cell radius . If a pair of terminals in two cells are using the same channel, the ratio is called the cochannel reuse ratio (CRR). What is the frequency reuse factor in CDMA Mcq? Explanation: The amount of out-of-cell interference determines the frequency reuse factor, f, of a CDMA cellular system. Ideally, each cell shares the same frequency and the maximum possible value of f (f=1) is achieved. What is i and j in cluster size? For hexagonal cells, i.e., with ‘honeycomb’ cell lay-outs commonly used in mobile radio, possible cluster sizes are C = i2 + ij + j2, with integer i and j (C = 1, 3, 4, 7, 9.). Integers i and j determine the relative location of co-channel cells. What will be the co-channel reuse ratio for a system where I j 2? What is the co-channel reuse value for a cluster size of 12? (c) For N = 12, total number of channels available per cell = 660/12 ≈ 55 channels. How is GSM calculated? The average weight of the specimen is 1.600 grams per 100 square centimeters. Now convert the weight into grams per square meters by multiplying the average weight by 100. Therefore, sample fabric GSM is 1.60 X 100 = 160 GSM. Why is frequency reuse important? Frequency reuse improve the spectral efficiency and signal Quality (QoS). Frequency reuse classical scheme proposed for GSM systems offers a protection against interference. What is the advantage of using frequency reuse? Explanation: Frequency reuse is a technique of reusing frequencies and channels within a cellular system to improve capacity and spectral efficiency. What is frequency reuse and co-channel reuse? If a pair of terminals in two cells are using the same channel, the ratio is called the co-channel reuse ratio (CRR). The frequency uses distance, D, (i.e., the distance between the two adjacent co-channel cells of radius R) is related to the number of cells in a frequency reuse pattern K. IS-95 has a frequency reuse factor of MCQ? In an IS-95 system, the frequency-reuse factor is normally _____. 128….Online Test. |125.||IS-95 uses the ISM _______band.| |d.||either (a) or (c)| What is the chip rate of W-CDMA? What is the chip rate of W-CDMA? Explanation: W-CDMA uses a chip rate of 3.84 Mcps. Chip rate is the product of symbol rate and spreading factor. What is the co-channel reuse ratio? What is the relation between co-channel reuse ratio & cluster size? |path loss exponent (meas)||n| |3.4||co-channel reuse ratio||sqrt(3N)| What are GSM types? The GSM network is divided into three major systems: the switching system (SS), the base station system (BSS), and the operation and support system (OSS). What is 250 GSM? 250 gsm paper is commonly used for greetings cards, invitations and booklet/brochure covers. 300 gsm/350 gsm. Thick board stock, ideal for book covers, business cards etc. This is our thickest available paper stock.

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https://scentregroup3rdquarter15.interactiveinvestor.com.au/9lhwa/fa288e-how-to-make-a-relative-frequency-histogram-in-google-sheets

math

Thanks! Can’t I start it with the value closer to my lowest data? The class upper limits then permit the use of the FREQUENCY function in spreadsheets such as Excel, LibreOffice.org, OpenOffice.org, Google Sheets and Gnumeric. To make the histogram for the above data, follow these steps: You should now see a histogram on your worksheet. I’d been a google sheets skeptic until I read through some of your posts. You do not have *smoothing* anymore in Google Sheets. comes up when I try to use the normdist formula for some values. Relative Frequency Graph Maker. Then open the Google Sheets with the data you want to use to make a histogram. If pie chart is made right click and select Change Chart Type, Bar Chart Click on a red bar and right click select Change Series Chart Type to Line Chart. We now need to calculate the distribution of the 1,000 exam scores for our histogram chart. But now, you can make one in a matter of seconds. On the Chart Editor pane, select the Histogram⦠For example, a shop might have a goal of selling 5% of their total items in the $41 â $50 price range. it has a longer tail on the left, more spread on the left. The new chart editor opens in a side pane, but the steps and options are essentially the same. We showed you why and how you can use a histogram. This was a great exploration for me, both in learning more advanced charts (advanced for me, at least!) I get a big tail of zeros by your method in Histogram 1 but everything else seems to work. On the Insert drop-down, click Chart. Highlight the entire data and click the + (Insert) sign on top of Google Sheets. The “Legend” category, as its name suggests, lets you provide settings and formatting for the histogram legend. Hi! Tally up the number of values in the data set that fall into each group (in other words, make a frequency table). Simply start with a blank chart or a histogram templates. As a starting point, you can take you max value (99.2 in this example) and min value (9.7 in this example), calculate the range between them (89.5) and then divide by how many bins you want to show (e.g. Make a title for the OY axis in a similar way. Create a named range from these raw data scores, called scores, to make our life easier. Adjusting the min and max inputs really helps you provide context to your histogram. Thank you, that was very helpful. Or, you can choose the smooth option in the customization menu: Hi Ben, Do you know how to make a histogram when I have a theoretical ‘Engagement Score’, a continuous variable, in Col A and counts of a given score in Col B? This thread is outdated. Your email address will not be published. How do array formulas work in Google Sheets? Should I always start my bins with 0? Google Sheets will insert a Column Chart. how did you come up with increments of 5 with the example that you used in the tutorial above? Formula to calculate relative frequency. ; From the add-on description page, click the "+Free" in the top right corner to add it ⦠Other Google Sheets tutorials you may like: Save my name, email, and website in this browser for the next time I comment. Your email address will not be published. you can easily understand the dynamics, trends, and relationships among data items and draw important inferences. When you click the + (Insert) sign, a drop-down will be displayed. Select the bins column and the Normdist column then Insert > Chart and select line chart, and make it smooth: That’s a normal distribution curve, around our mean of 56.9. This category lets you provide the text and formatting for the chart title and subtitle as well as the titles for both x and y axes. Make it count Google Sheets makes your data pop with colorful charts and graphs. To make a histogram, you first divide your data into a reasonable number of groups of equal length. This tool will create a histogram representing the frequency distribution of your data. So we can set the legend position to none. However, after the creation of the ND, I see false input in the Advanced settings’ Chart types’ first box where is only one column, while I expect there to be two columns. Bit of a mouthful, but in essence, the data converges around the mean (average) with no skew to the left or right. If you want to create histograms in Excel, youâll need to use Excel 2016 or later. Select the data you want to visualize in your histogram. The last bin gives the total number of datapoints. In column I, let’s use the FREQUENCY formula to assign our 1000 scores to the frequency bins. You should see an ellipsis (or hamburger icon) on the top right corner of the box containing the graph. Google Sheets Developer & Data Analytics Instructor. Series: Change bar colors. You can choose the smooth line chart option in the chart choose menu: 2. This is super helpful, not simple. How can I make it work? The third column is for the count or frequency of data in each class. Histograms are a useful tool in frequency data analysis, offering users the ability to sort data into groupings (called bin numbers) in a visual graph, similar to a bar chart. Select the Smooth option: Select the vertical axis. To plot the Histogram chart, first, select the whole data in column A and go to the menu Insert > Chart. So you plot how data of a single category is distributed. A survey – Zubair Lutfullah Kakakhel, http://datapigtechnologies.com/blog/index.php/understanding-standard-deviation-2/, Does GPA matter for my salary? Double-click the chart you want to change. I myself have a similar data but I choose graphically those two columns with their titles (like you do in Excel) and do Chart > Line > …. Copy the raw data scores from here into your own blank Google Sheet. A histogram is the best chart you can use to illustrate the frequency distribution of your data. It’s advisable for them to be whole numbers too, both aesthetically and to ease understanding. Let me help you with Google Sheets and Apps Script. It allows you to see the proportion or percentage that one value is repeated among all the elements in the sample. What if you are trying to compare your data not to the normal distribution of your data, but say the district’s average? Is the Scale Factor 0.39 (78 * 0.005)? If we look closely, it’s skewed very, very slightly to the left, i.e. Then, edit the chart data through the spreadsheet editor - Just replace the values by typing in your own data set. (ie. Let’s set up the normal distribution curve values. After selecting a combo chart, I am not getting the “Smooth” option. Thank you for a tutorial that was clear and concise. However you should not truncate the y-axis (vertical axis) because the height of the bars is measured from zero and this prevents the data being distorted. However, sometimes the Chart editor goes away after your histogram has been created. This could sometimes help make the histogram easier to read and understand. Enter âRelative Frequencyâ in cell C1. The data I have is at an aggregate level and instead of Engagement Score of 18.8 listed out in 1,000 rows, I simply have a2 = 18.8 | b2 = 1000. This is a great article that goes into more detail about standard deviations: http://datapigtechnologies.com/blog/index.php/understanding-standard-deviation-2/. ), 1) The P at the end of STDEVP stands for population and should be used for calculating standard deviations on whole populations, as opposed to when you’re looking at samples (when you’d use the regular STDEV function). To understand how to create a histogram, we are going to use the data shown in the image below: This dataset contains scores of students in an exam. For example, if you had to compare the distribution of marks for two different classes, you could use one color for grade 6 and another for grade 7 (say). Meaning, when I multiply the normal distribution values by 5,000, they’ll be comparable to the histogram values on the same axis. Can you please be precise and say how you choose the data in the step six? A relative frequency histogram is a graph that displays the relative frequencies of values in a dataset. The #NUM! Some other settings available under these categories include: Finally, you can format the histogram to contain major and/or minor gridlines. It says “…the averages of random variables independently drawn from independent distributions converge in distribution to the normal…” What does this mean? A histogram is one such helpful visualization tool that helps you understand the distribution of your data. (Or just click the link here). It divides the range of your data into intervals, displaying how many of the data values fall into each interval. Can you please be more precise on the step 6 because I cannot reproduce your method. In our example, we changed the background color to “light green 3”, and allowed the other settings to remain the same. The kind of data plotted by histograms and Bar Graphs is also different. Its calculations, however, are usually far from perfect. Raw data. To make the histogram for the above data, follow these steps: We want to create a histogram to understand how the student scores in the exams were distributed. For example, you can use it to give a title for the vertical axis, by selecting the “Vertical axis title” option from the dropdown menu and then set the title as “Student Count”. If a data point falls on the boundary, make a decision as to which group to put it into, making sure you stay consistent (always put it in the higher of the two, or always put it in the lower of the two). The normal distribution curve is a graphical representation of the normal distribution theorem stating that “…the averages of random variables independently drawn from independent distributions converge in distribution to the normal, that is, become normally distributed when the number of random variables is sufficiently large”. A survey | cloud5, How to Create a Scatter Plot in Google Sheets. Hope you have the data to plot the Histogram Chart in Google Sheets now. Paste the frequency distribution into cell A1 of Google Sheets so the values are in column A and the frequencies are in column B. Last updated: October 12, 2017 [Download PDF]What are Histograms? You can use it to count the frequency of values in a range. This range is actually called a one column array. Before Excel 2016, making a histogram is a bit tedious. At the right, click Customize. We need to scale our normal distribution curve so that it’ll show on the same scale as the histogram. Creating a Histogram in Google Sheets. Type into the field the number for the bucket size that you would like represented in the histogram. FREQUENCY Function in Google Sheets. As such, you will usually feel the need to customize the histogram to give it the look and functionality you want. In this tutorial, I will show you how to make a histogram in Google Sheets and how to customize it. We expect our exam scores will be pretty close to the normal distribution, but let’s confirm that graphically (it’s difficult to see from the data alone!). Begin with a column that lists the classes in increasing order. To make it appear again and to customize your histogram, do the following: The Chart style category in the Chart editor lets you set the background color, border color, font style, and size of your chart. What’s the average score? You have two options: 1. With the help of visualization tools like charts, graphs, maps, etc. We expect 68% of values to fall within one standard deviation of the mean, and 95% to fall within two standard deviations. How clustered around the average are the student scores? Highlight all the data in column A, i.e. Seems the new chart editor does not have the “smooth” option for the combo charts, but you can click “Use the old chart editor” at the bottom of the sidebar to go back to the old editor which does still have the smooth option. Itâs a list of 1,000 exam scores between 0 and 100, and weâre going to look at the distribution of those scores. One quick note – I think the text for normal distribution theorem should be slightly different? On your computer, open a spreadsheet in Google Sheets. 3) Good question. Fantastic tutorial. While in Excel and LibreOffice.org the existence of a gap width or spacing setting allows the columns to touch, Google Docs did not provide this option, hence the chart seen below. Insert Histogram Chart in Google Sheets. Usually, the Chart editor has a ‘Customize’ tab that lets you enter all your specifications. In our example, it would make sense to distribute the scores between 0 and 100. Create a new Google Spreadsheet (or open an existing one) From the menu bar, choose: Add-ons -> Get Add-ons. Google Sheets performs its own calculations on your data and displays what it believes to be the optimal number of bins for your histogram. Distributions were in intervals of 10 let ’ s set up the normal distribution theorem should be different., youâll need to use for the bucket size that you would represented!: October 12, 2017 [ Download PDF ] what are histograms ( an Easy Guide ) represented in sample... Alongside the normal distribution curve and to ease understanding normal distribution or choose to not have * smoothing anymore... Edit or format title text been a Google Sheets performs its own calculations on your.! You able to do this using the native histogram charts in Google Sheets,... Understand the distribution of data points per bin to distribute the scores between 0 and 100, if! Api, run kstest on the x-axis to be a range, like 0-9 %, %... Sample, with respect to the frequency, so it would be better if the distributions were intervals... Could sometimes help make the histogram for the tutorial above a normal sheet table of frequencies a! When youâre interested in percentage values precise and say how you can ’ t I start it with native., http: //datapigtechnologies.com/blog/index.php/understanding-standard-deviation-2/ cover your whole dataset you might want to create a new Google spreadsheet ( hamburger. Is one such helpful visualization tool that helps you understand the distribution of data... Or change bucket size that you used in the chart choose menu: 2 above... Get Add-ons the cell range A1: A12 skewed or just all over the place of bins... That plots frequency distribution shows how a variable is distributed available under these categories include:,! Actually called a one column Array dashboards and reports own blank Google sheet Apps. Just checked now and the normal distribution function for a property for your histogram one quick note – think! Clustered around the average are the “ legend ” category, as name... To draw the histogram chart usually feel the need to customize the histogram frequencies is particularly good displayed in tutorial... Can be interpreted as probabilities ticks at how to make a relative frequency histogram in google sheets, to make a histogram a! To reflect every little change you made alongside the normal distribution called scores, bins ) ) ` not! But the steps and options are essentially the same size and cover your dataset... The mean, our scale factor is 5,000 copy this column of frequency instead of COUNTIFS fill... Enter all your specifications PDF ] what are histograms a survey | cloud5, how much I! Apps Script determining if your data is normally distributed, skewed or just all over the place frequencies values. It easier in perceiving, analyzing the results and presenting them to be whole numbers too both. You plot how data of a bar graph life easier to relative frequency histogram is when! Increments of 5 function in Google Sheets etc. is a great exploration me. Top right corner of the data you ’ re free to choose sensible sized (. For determining if your data and Move to a normal sheet together with frequency do not have * smoothing anymore. Exploration for me to get the range of your data into a reasonable number of in. Points in the exams were distributed menu: 2 Edit the chart opens... You please be more precise on the same and formatting for the histogram chart blank Google sheet illustrate... The whole data in column B http: //datapigtechnologies.com/blog/index.php/understanding-standard-deviation-2/ the min and max to do this to get labels... Our normal distribution theorem should be slightly different click the + ( Insert ) sign top... Did you come up with increments of 5 be better if the were. Gridlines to be able to create a histogram, which allows for a property axis! Could have different colors for different series, and set the major gridlines 4... And Apps Script of COUNTIFS to fill up the histogram easier to read and understand change bucket that. Chooses the number of bins for your histogram line chart option in the data you want bins! Chooses the number of data in each class your requirement size you get the range perceiving, analyzing the and... Editor has a longer tail on the left, more spread on the same scale as the and! Contain major and/or minor ticks on your data is very close to lowest!, https: //productforums.google.com/forum/ #! topicsearchin/docs/category $ 3Aspreadsheets, Does GPA matter for my salary s for. These categories include: Finally, you can format the histogram from the menu >... For this, you will usually feel the need to change the scale factor 0.39 ( 78 0.005. Have * smoothing * anymore in Google Sheets and Apps Script Google spreadsheet ( open... Get a big tail of zeros by your method in histogram 1 but everything else seems work. Determine what increments to use for the “ charts ” tab of the normal distribution columns: show dividers... Horizontal axis category to change the min and max to do this in shortly ) let! Right corner of the Google Sheets API, run kstest on the left, more on. Event or category of data in each class ) how do you determine what increments to use the histogram the! Optimal number of times each category how to make a relative frequency histogram in google sheets in the chart choose menu: 2 are marked *, Learn about. Values for the bucket size that you used in the histogram for the above data, while bar! Usually far from perfect without seeing your data that category at least ). They ’ ll show on the other hand, plot categorical data by counting the of! YouâLl need to use to make our life easier Google spreadsheet ( or hamburger icon on! This for our histogram chart in Google Sheets the number for the OY axis in a.. Size that you how to make a relative frequency histogram in google sheets like represented in the histogram to understand how the chart editor goes away after histogram. Determining if your data option: chart style: change how the student scores the! Survey – Zubair Lutfullah Kakakhel, http: //datapigtechnologies.com/blog/index.php/understanding-standard-deviation-2/, Does GPA matter my... One column Array values for the tutorial ) equal length us the frequency bins are histograms to cell.! Statistics add-on from the Add-ons gallery and select it I think the text for distribution. Bins, displaying how many values occurred close to the menu Insert >.. Scale our normal distribution theorem should be slightly different: type category histogram Google! Data to be how to make a relative frequency histogram in google sheets optimal number of bins for you now the basics and done do following. Tutorial above step 6 because I can not reproduce your method in histogram 1 but everything else seems to.. Why and how you choose the Smooth option is definitely still available your.! On your worksheet steps and a few seconds then you could have different colors different! See a histogram in Google Sheets skeptic until I read through some of posts... Sheets ( an Easy Guide ) axis in a Microsoft spreadsheet in Google Sheets by calculating the distribution! Were in intervals of 10, more spread on the left, i.e an Easy Guide ) min max... ( not too narrow, not too narrow, not too wide ) increments to use for above. And displays what it believes to be, or choose to not have them at all made a... Classes in increasing order Polygon '' box to show the old chart editor ] histogram Maker normal distribution columns histogram... Replace the values by typing in your histogram has been created the vertical axis and bar graphs is also.! From a bar graph the general distribution of your posts item in the histogram from the how to make a relative frequency histogram in google sheets example we. Dividers checkbox lets you provide context to your liking or ‘ buckets ’ will be updated instantly to every. A kind of data, follow these steps: create the histogram legend position to.... Values into the field the number for the histogram: show item,... A category is distributed ( advanced for me, at least! draw the histogram of. Me become way more productive charts ” tab of the 1,000 exam scores for our histogram.! Set and format major and/or minor ticks on your data pop with charts! Along the x-axis have very arbitrary sizes me to get the range of your.... The use of frequency instead of COUNTIFS to fill up the normal distribution theorem should slightly! Editor opens in a range of values in a sample, with respect to the mean else seems to.. Of this template > > like charts, graphs, maps,.... Which you want to visualize in your histogram ’ s helped me become more! Up the frequency of data points per bin #! topicsearchin/docs/category $ 3Aspreadsheets, GPA! And understand updated: October 12, 2017 [ Download PDF ] what are histograms that! Learned how to make a title for the Horizontal axis category to change the and. 12, 2017 [ Download PDF ] what are histograms and select it like bars of a of... Allows you to compare how often values occur relative to the lowest provided! Frequency, and change the range named range from these raw data scores here. A level of automation [ ⦠] histogram Maker displaying how many values occurred to... How did you come up with increments of 5 we showed you why how... Visualizations of your data you add a line between each item in chart. Up when I try to use the function ArrayFormula together with frequency use to make a,! That lists the classes in increasing order m not getting the “ legend ” category as!

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CC-MAIN-2021-39

http://pscourseworkswuk.rossienginesusa.us/capacitor-and-equivalent-capacitance.html

math

A guide to calculating the capacitance of capacitors when used how to calculate capacitors in series and parallel how to calculate capacitors in series and parallel. I have a 125v 2ah battery and i'm trying to calculate a equivalent capacitance with rated voltage of 27v for each of those batteries this is what i did: work of battery = \$125v \cdot 2a. Capacitors in series and in parallel next: the equivalent capacitance of two capacitors connected in parallel is the sum of the individual capacitances. Multiple connections of capacitors act like a single equivalent capacitor the total capacitance of this equivalent of capacitors in series and parallel. Capacitors are passive devices used in electronic circuits to store energy in the form of an electric field they are the compliment of inductors, which store energy in the form of a. Three capacitors are connected in series the equivalent capacitance of this combination is 318 f two of the individual capacitances are 654 f and 819 f. This is a series and parallel capacitor calculator it computes the total capacitance value of a circuit, either of capacitors in series or in parallel. It's all about charge, voltage, and capacitance in exactly the opposite way as resistors in series and parallel are all about voltage, current, and resistan. Answer to capacitors in series: find (a) the equivalent capacitance, (b) the charge on each capacitor, (c) the voltage across each. Combine capacitors in parallel calculating the total capacitance of two or more capacitors in electronics components: capacitors in the circuits are equivalent. Ap physics practice test: capacitance, resistance capacitor with capacitance c the equivalent capacitance of the three capacitors is. Types of capacitor, definition of capacitors, storing charge, charging and discharging, dielectric constant, capacitors series and parallel. G12: capacitance revision study play how is the equivalent capacitance of a parallel combination in a parallel-plate capacitor capacitance is directly. This video guides you through the steps in finding the equivalent capacitance of a basic circuit the circuit contains 11 capacitors in total like us on f. Capacitors in series and parallel let us see how to calculate the equivalent capacitance of capacitors when connected in parallelconsider two capacitors. Esr equivalent series resistance the esr rating of a capacitor is a rating of quality a theoretically perfect capacitor would be lossless and have an esr of zero. Electronics tutorial about connecting capacitors in series including how to calculate the total capacitance of series connected capacitors. Capacitors experiment we can find the equivalent capacitance value capacitor and determine its capacitance by measuring v 2 and using equations 1 and 3. For this final equivalent capacitor with capacitance c eq2, the voltage across it is, of course, 120 v the charge on this capacitor, q eq2, is. Question: a and a capacitor are connected in parallel, and this pair of capacitors is then connected in series with a capacitor, as shown in the diagram what is the equivalent capacitance. When capacitors are connected in series, the total capacitance is less than any one of the series capacitors’ individual capacitances if two or more capacitors are connected in series, the. Capacitance, insulators, dielectrics, capacitors, capacitors in series, capacitors in parralel, energy stored in a capacitor. The canonical definition for capacitance between two nodes, whether total, equivalent or other, is the charge in coulombs required to change the potential difference by one volt. The capacitance of a capacitor is proportional to the surface area of the plates the earliest unit of capacitance was the jar, equivalent to about 111 nanofarads. Chapter 5 capacitance and dielectrics figure 57: (a) series capacitors in previous figure have been combined as a single equivalent capacitor (b. Capacitors in series and parallel systems including capacitors more than one has equivalent capacitance capacitors can be connected to each other in two ways. First i calculated equivalent capacitance between r and m the two 2μf capacitors are in series their combination is in parallel with the 1μf capacitor their equivalent capacitance is. Capacitors and rc circuits when capacitors are arranged in parallel when capacitors are arranged in series, the equivalent capacitance is. Formula of equivalent capacitance in series series combination when capacitors are connected in series,the total capacitance is less than the smallest capacitance value because the. Capacitors in parallel capacitors can be connected in parallel: the equivalent capacitance for parallel-connected capacitors can be calculated as. Practice problems: capacitors solutions 1 (easy) determine the amount of charge stored on either plate of a capacitor (4x10-6 f) when connected across a 12 volt battery c = q/v. Answer to: how to find equivalent capacitance of a network of capacitors by signing up, you'll get thousands of step-by-step solutions to your. For an arbitrary number of series-connected capacitors the charge is the same on each capacitor and the equivalent capacitance is determined from. All Rights Saved.

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CC-MAIN-2018-34

https://www.nagwa.com/en/videos/404191750759/

math

To roast a chicken, it should be cooked in the oven at 325 degrees Fahrenheit for 20 minutes per pound plus an additional 20 minutes. If a chicken takes one and a half hours to roast at 325 degrees Fahrenheit, write an equation that you could use to find 𝑤, the weight of the chicken. One and a half hours is equal to 60 minutes plus 30 minutes, as there are 60 minutes in one hour. This means that the total cooking time was 90 minutes. We were told in the question to let 𝑤 be the weight of the chicken. It takes 20 minutes to cook per pound. This is equal to 20𝑤. The chicken also needs to be cooked for an additional 20 minutes. Therefore, an expression for the total cooking time is 20𝑤 plus 20. This particular chicken took 90 minutes to cook. Therefore, the equation is 20𝑤 plus 20 is equal to 90. We could then use this equation to work out the weight of the chicken. Subtracting 20 from both sides of the equation gives us 20𝑤 is equal to 70. Dividing both sides of this equation by 20 gives us 𝑤 is equal to 70 divided by 20. We can simplify this fraction by dividing the numerator and denominator by 10. This leaves us 𝑤 is equal to seven divided by two. Seven divided by two is equal to 3.5. Therefore, the weight of the chicken is 3.5 pounds.

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CC-MAIN-2021-04

https://centregalilee.com/what-does-the-e-on-the-calculator-mean/

math

You are watching: What does the e on the calculator mean TL;DR (Too Long; Didn"t Read) On a calculator display, E (or e) represents exponent that 10, and also it"s always followed by another number, which is the value of the exponent. Because that example, a calculator would display the number 25 sunshine as either 2.5E13 or 2.5e13. In other words, E (or e) is a short type for scientific notation. Science is complete of very big and very little numbers that are an overwhelming to read and write. For example, the massive of the earth is 5,970,000,000,000,000,000,000,000 kilograms, while the massive of a hydrogen atom is 0.00000000000000000000000000167 kilograms. Clinical notation makes these numbers much easier to take care of by expressing the 0"s as a power of ten. Utilizing this notation, the mass of the earth becomes 5.97 × 1024 kg, and also the fixed of a hydrogen atom i do not care 1.67 × 10-27 kg. Rather of numbers with long strings the zeros the are complicated to count and even more daunting to display screen on a tiny screen, you have much more manageable decimal fractions and exponents the 10. In its created form, clinical notation would certainly look strange on a calculator. It would be confusing and it wouldn"t to the right on a small display. To protect against these problems, manufacturers developed a symbol for "X 10." This prize is one of two people E or e, depending on the calculator. This letter is constantly followed by a number, which is the exponent to which 10 is raised. On a calculator display, the massive of the earth would be presented as 5.97E24 (or 5.97e24). The number 5.97 is the argument and also the number 24 is the exponent. Similarly, the mass of a hydrogen atom would certainly be 1.67E-27 (or 1.67e-27). It"s simply as complicated to beat in long strings the zeroes ~ above a calculator pad as it is to create them on paper, so must calculators have actually a shortcut. It"s the EE key. To get in a number in clinical notation, an initial input the argument, then push the EE an essential and go into the exponent. For example, to go into the mass of the earth, crucial in 5.97, then push the EE key and enter 24. The display screen will read 5.97E24 (or 5.97e24). Keep in mind that the number will show up with all its zeroes if castle fit on the screen. Because that example, if you crucial in 1.2 EE 5, the display screen will present 120,000. Most scientific calculators devote a special key to Euler"s number, because it is among the most important irrational number in mathematics and also enters right into all kinds of scientific calculations. This is the "e" key. Push it, and Euler"s number will appear in your display to the accuracy the screen allows. The scientific calculator on an iPhone, because that example, reflects 2.718281828459045. In addition, most calculators likewise have one "ex" key. Get in a number, push this vital and the display screen will display the worth of e elevated to the exponent you entered. In neither of these cases does "e" have the same definition as it does when it appears in the display. See more: What Is The Area Under A Velocity Vs Time Graph, What Are Velocity Vs Chris Deziel hold a Bachelor's level in physics and a Master's level in Humanities, He has actually taught science, math and also English at the university level, both in his aboriginal Canada and also in Japan. He began writing virtual in 2010, offering information in scientific, social and valuable topics. His creating covers science, math and home improvement and design, and religion and also the eastern healing arts.

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CC-MAIN-2022-21

https://www.slideshare.net/Annajab/network-topologies-network-devices

math

• What is a Topology ? • The physical topology of a network refers to the configuration of cables, computers and other Types of Topologies • Popular on LANs because they are inexpensive and easy to • Consists of a main run of cable with a terminator at each end • All computers and devices connected to central cable or • Primarily is used for LANs, but also is used in WANs. • Data travels from device to device around entire ring, in • Cable forms closed ring or loop, with all computers and devices arranged along ring. • A network setup where each computer and network device is interconnected with one another. • This topology is not commonly used for most computer networks as it is difficult and expensive. • A tree topology combines the characteristics of bus and star • It consists of different groups of computers attached in star topology. • The groups are then connected to a bus backbone cable. • Tree topology is used for the expansion of an existing network. • A combination of two or more different topologies makes a hybrid topology. • One of the prominent advantages of this topology is its flexibility • Since different topologies come together in a hybrid topology, managing the topology becomes difficult. • It is also very expensive to maintain.

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CC-MAIN-2018-22

https://en.m.wikibooks.org/wiki/Basic_Algebra/Polynomials/Zero_and_Negative_Exponents

math

Basic Algebra/Polynomials/Zero and Negative Exponents There are two very important things you need to know when working with Zero Power or Negative Exponents. First, any number to the Zero Power always equals one. For example (-50)0 = 1 There is one number that CANNOT be raised to the Zero Power, 00 does not exist! When dealing with Negative Exponents there is a simple trick. Whatever part of a fraction the negative exponent is in, switch it and the exponent becomes positive. a-2 = 1/a2 1/a-3 = a3 If we have something a little more complicated, we only move things with Negative Exponents. These processes only work with multiplication. If there is addition/subtraction involved, then we are in something a little more complicated than Algebra 1... (a-2c3)/b-1 = (bc3)/a2 Something like this wouldn't follow the aforementioned rules (a-2 + b5)/(c6) This problem would require a little more work: splitting up the fraction and working with both parts individually and having an answer with two fractions instead of one nice one. It's possible but it doesn't flow like the other examples or the practice problems. (-2)2 = 4. -22 = -4. ^ for exponentiation

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CC-MAIN-2021-17

https://cracku.in/ibps-clerk-2014-question-paper-solved?page=4

math

Study the following information to answer the given questions. Ten people are sitting in two parallel rows having five people each, in such a way that there is an equal distance between adjacent person. In row 1-V, W, X, Y and Z are seated (but not necessarily in the same order) and all of them are facing North. In row 2-F, G, H, I and J are seated (but not necessarily in the same order) and all of the are facing South. Therefore, in the given seating arrangement, each member seated in a row faces another member of the other row. • Y sits third to the left of W. The one who faces Y sits second to the right of F. • Only one person sits between F and I. • H and J are immediate neighbours of each other. J does not sit at any of the extreme ends of the line. • The one faces G sits to the immediate right of Z. • X is not an immediate neighbour of Z. These questions consist of a question and two statements numbered I and II below it. You have to decide whether the data given in the statements are sufficient to answer the questions. Read the statements and choose the most appropriate option. In a straight line of eight people (all facing North), what is the position of R from the left end? I. Y stands fourth from the right end of the line. Only two people stand between Y and Z. R stands to the immediate right of Z. II. W stands fourth from the left end of the line. R is an immediate neighbour of W.

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http://www.stsci.edu/hst/HST_overview/documents/synphot/c022.html

math

Synphot Data User's Guide 2.1 Ramp filters (ACS, WFPC2) Fifteen ramp filters are available for use with the WFC detector, and six are available for use with the HRC detectors. To use the ramp filters in simulations, use the keyword syntax ffff#wwww, where ffff is the filter and wwww is the desired central wavelength, specified in Angstroms, e.g., obsmode=" Filter wheel 12 contains four linearly variable narrowband ramp filters, which together cover a total wavelength range of 3700 to 9800 Å. The FWHM of the throughput at a given wavelength is typically about 1% of the central wavelength. The ramp filters have been implemented as a parameterized component in synphot. To use the ramp filters in simulations, use the keyword syntax lrf#wwww, where wwww is the desired central wavelength,, specified in Angstroms, e.g., obsmode=" Space Telescope Science Institute Voice: (410) 338-1082

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CC-MAIN-2018-05

https://van.physics.illinois.edu/qa/listing.php?id=2825

math

Your question seems to presume that the old Bohr attempt at a quantum theory is correct, which is very far from true. In Bohrís picture, an electron would sit in a state with definite energy (e.g. a íshellí state) then suddenly jump to a state with a different definite energy. In actual quantum mechanics, the time-dependent state will change in a gradual, continuous manner, at least as far as it is described by the SchrŲdinger equation. If ímeasurementí processes occur, what happens on the way to a definite perceived outcome is controversial. The predicted distributions of observed measured outcomes if the experiment is repeated many times is not controversial, however. Anyway, letís get to your last question: whether itís the same electron at the beginning and end. Thereís a definite sense in which it is, because the quantum state of the beginning electron has changed in a continuous way to that of the final one. However, it is a little misleading to think of electrons as having identities. Consider a helium atom with two electrons, in the same íshellí. They have opposite spins. You might think that this constitutes two states: either up-down or down-up, depending on which electron is which. However, nature tells us which states it considers different via statistical mechanics, and the He atom has just one ground state. The electrons donít have identities. (published on 10/22/2007)

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CC-MAIN-2017-17

https://essays-writings-service.com/2020/09/25/how-to-solve-algebra-2-problems_wm/

math

Up next. 8. take the results of step 5 and use assignment constructor the algebra skills you’ve learned to solve the problem. click or tap the select reading book essay an action box and then choose the solving chemical equilibrium problems action the help movie free online you want math assistant to take. 2. 78k online math problem solver thomas edison essay https://www.math10.com/en/problem-solver online algebra solver i advice you to sign up for do you have to write a dissertation for masters this algebra solver. here are some tips for getting a solid system of steps to follow when background paragraph argumentative essay you are solving algebra word problems: 5(x − 3) = 0. how to solve algebra 2 problems above, you learned that how to solve algebra 2 problems to find 200% of any number, you just multiply that number by 2: linear equations – solve for x in the following equations. the question verifies that you don’t know how many weeks.

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CC-MAIN-2021-10

https://fossilhuntress.blogspot.com/2020/09/fossil-fuels-and-earths-mass.html

math

Well, Melaina, the Earth’s mass does decrease when fossil fuels are burnt. But not in the sense you were probably imagining, and only to a very, very small degree. There is no decrease in chemical mass. Burning fossil fuels rearranges atoms into different molecules, in the process releasing energy from chemical bonds, but in the end, the same particles — protons, neutrons, and electrons — remain, so there is no decrease in mass there. But energy is released, and some of that energy is radiated out into space, escaping from the Earth entirely. Einstein's Theory of Relativity tells us that energy does have mass: E=mc^2, or m=E/c^2. When a chemical bond that stores energy is formed, the resulting molecule has a very tiny bit more mass than the sum of the masses of the atoms from which it was formed, so a net gain. Wait, what? Again, this is an exceedingly tiny bit. In very rough numbers, worldwide energy consumption is about 160,000 terawatt-hours per year, and about 80% of that comes from fossil fuels. That is about 450,000,000 TJ/year (tera-joules/year). The speed of light is 300,000,000 meter/s; dividing 450,000,000 TJ by (300,000,000 m/s)^2 gives a decrease in mass of 5000 kilograms per year. That is an exceedingly small fraction — 50 billionths of one percent — of the approximately 10,000,000,000,000 kilograms of fossil fuels consumed per year. And as far as making the Earth lighter, it’s a tenth of a billionth of a billionth of a percent of the Earth’s mass. Of course, the energy in fossil fuels originally came from the Sun, and in absorbing that sunlight the Earth’s mass increases slightly. I picture the Earth expanding and contracting, taking a deep breath, then exhaling. We don't see this when we look, but it is a great visual for imaging this never-ending give and take process. I'm not sure how we'd measure the small changes to the Earth's net mass on any given day. The mass of the Earth may be determined using Newton's law of gravitation. It is given as the force (F), which is equal to the Gravitational constant multiplied by the mass of the planet and the mass of the object, divided by the square of the radius of the planet. Newton's insight on the inverse-square property of gravitational force was from an intuition about the motion of the earth and the moon. The mathematical formula for gravitational force is F=GMmr2 F = G Mm r 2 where G is the gravitational constant. I know, Newton’s law could use some curb appeal but it is super useful when understanding what keeps the Earth and other planets in our solar system in orbit around the Sun and why the Moon orbits the Earth. We have Newton to thank for his formulas on the gravitational potential of water when we build hydroelectricity dams. Newton’s ideas work in most but not all scenarios. When things get very, very small, or cosmic, gravity gets weird... and we head on back to Einstein to make sense of it all. There was a very cool paper published yesterday by King Yan Fong et al. in the journal Nature that looked at heat transferring in a previously unknown way — heat transferred across a vacuum by phonons — tiny, atomic vibrations. The effect joins conduction, convection and radiation as ways for heating to occur — but only across tiny distances. The heat is transferred by phonons — the energy-carrying particles of acoustic waves, taking advantage of the Casimir effect, in which the quantum fluctuations in the space between two objects that are really, really close together result in physical effects not predicted by classical physics. This is another excellent example of the universe not playing by conventional rules when things get small. Weird, but very cool! But the question was specifically about the mass of the Earth and the burning of fossil fuels, and that process does decrease the mass. So it is mostly true that the Earth’s mass does not decrease due to fossil fuel burning because the numbers are so low, but not entirely true. The fuel combines with oxygen from the atmosphere to produce carbon dioxide, water vapour, and soot or ash. The carbon dioxide and water vapour go back into the atmosphere along with some of the soot or ash, the rest of which is left as a solid residue. The weight of the carbon dioxide plus the water vapour and soot is exactly the same as the weight of the original fuel plus the weight of the oxygen consumed. In general, the products of any chemical reaction whatsoever weigh the same as the reactants. There is only one known mechanism by which Earth’s mass decreases to any significant degree: molecules of gas in the upper atmosphere (primarily hydrogen and helium, because they are the lightest) escape from Earth’s gravity at a steady rate due to thermal energy. This is counterbalanced by a steady rain of meteors hitting Earth from outer space (if you ever want to hunt them, fly a helicopter over the frozen arctic, they really stand out), containing mostly rock, water, and nickel-iron. These two processes are happening all the time and will continue at a steady rate unchanged by anything we humans do. So, the net/net is about the same. So, the answer is that the Earth's mass is variable, subject to both gain and loss due to the accretion of in-falling material (micrometeorites and cosmic dust), and the loss of hydrogen and helium gas, respectively. But, drumroll please, the end result is a net loss of material, roughly 5.5×107 kg (5.4×104 long tons) per year. The burning of fossil fuels has an impact on that equation, albeit a very small one, but an excellent question to ponder. A thank you and respectful nod to Les Niles and Michael McClennen for their insights and help with the energy consumption figures.

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CC-MAIN-2021-17

https://generatingfunctions.wordpress.com/2015/05/01/permutations-combinations-and-why/

math

We’ve spent a couple of days in precal talking about permutations and combinations. The first day, we did a fairly straight-forward permutations/combinations lesson. How many ways can you arrange 5 cars in a driveway? How many distinguishable arrangements of the letters in the your full name are there? (Most people have at least one repeated letter.) How many 3-letter “words” can you form if you never repeat a letter? If you only use consonants? If you only use vowels? If I have ten books and want to take 3 on a trip, how many different sets of 3 do I have to choose from? It was a fairly standard lesson. We’d arrange 2 cars, then 3, then they’d arrange 4 cars, then we’d find the pattern and make predictions. What was slightly different (and what I want to do more of) is this: when we found the pattern, I’d make them figure out why. If they couldn’t, I’d help, but they had to try on their own first. Why is the number of ways you can arrange 4 cars equal to 4*(the number of ways you can arrange 3 cars)? Why would we divide by the factorial of the number of times a letter is repeated in your name? Repeat with each different topic. When we hit permutations and combinations, I introduced the vocabulary, as well as the notation and the phrase “binomial coefficient.” Today, we did Pascal’s Triangle. We started by expanding binomials: … . I wrote the coefficients in a triangle, they saw the pattern, and we expanded more binomials. Then I had them compute binomial coefficients, and we arranged them in a triangle. They caught on pretty quickly to the fact that the binomial coefficients we’d computed on Wednesday were, in fact, the coefficients of expanded binomials. Then I asked why. Why would it be true that the coefficient of in the expansion of would be the same as the number of ways to choose 3 items out of 4? I got a lot of blank stares, so I told them to talk about it with their neighbors for five minutes. I wandered the classroom and listened to their discussions (they’re very used to this), and I realized that almost all of them were stuck. After about four minutes, I called it, and we went back to a large group. One pair of students came up with a pretty good explanation. They had trouble phrasing it, so I helped a bit. Most of them understood it when I explained it, although they said they couldn’t explain it yet themselves. That’s not a total victory, but I had to leave it there for the day. The most interesting part of class for me, though, was when one girl said, “Ugh! This is math class! I’m not supposed to have to answer why!” I ask students to explain and justify their answers, although I probably ask that more in Calculus than in Precal. That’s something that I’ll need to work on for next year. But the beautiful thing about math is that there is a why, that things can be proven. Lots of my students want to tell me, “Because that’s just how it is!” or “Because God made it that way!” when I ask them to explain why. That’s true, but that’s not a reason. Math, more than any other subject, always has a reason. I’m not sure how to address this misconception, but it’s something I want to change.

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http://teatrkoku.info/?krjl=870

math

1 Factoring polynomialsAlgebra 2 Polynomials radical. Perhaps the most important pattern to be gained from these two examples that will help us factoring in our future work in factoring trinomials concerns the signs in the products Factoring Trinomials Worksheet Answers wiildcreative Graph Art Worksheets Acceleration Worksheet Middle School Subtracting Decimals Worksheet 5th Grade Subtracting Whole Numbers Worksheets Physical Activity Worksheets Math Maze Worksheets Union Intersection Of Sets Worksheet Simplifying Radicals Worksheet Figurative Language Quiz Worksheet SparkNotes: Algebra II: Factoring Summary Analysis. For example for 24 the GCF is 12. We played this matching game then I gave them. Algebra Students Math Great Factoring Trinomials Practice for my Algebra students factor by grouping polynomials calculator Softmath here are two more formulas to handle special cases of cubic polynomials: eqnarray26. Factor the polynomial identify it as irreducible. Some of the trinomials have leading coefficients which can be factored out in some cases must be left in for other problems Understanding Algebra: Why do we factor equations. Students will factor the trinomialswith then they will color , withouta ) completely draw on the penguin as indicated by their answer. comIn this lesson such Factoring trinomials Basic mathematics Learn factoring trinomials , students learn that a trinomial in the form x 2 bx cwhere c is negative polynomials made up of three terms. This lesson is Factoring Trinomialsa 1) Read reviews compare customer ratings, see screenshots learn more about Socratic Math Homework Help. Factoring TrinomialsUsing Diamond Problems : Algebra Helpsolutions examples videos) Online Math Learning Polynomials. It s a great way to review to learn along with your class Math Review of Factoring Polynomials. We will add subtract, multiply even start factoring a polynomial. 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CC-MAIN-2018-47

https://projecteuclid.org/euclid.ade/1355867256

math

Advances in Differential Equations - Adv. Differential Equations - Volume 14, Number 5/6 (2009), 433-476. Degenerate parabolic equation with critical exponent derived from the kinetic theory, I, generation of the weak solution We study a degenerate parabolic equation derived from the kinetic theory using Rényi-Tsallis entropy. If the exponent is critical, we have the threshold mass for the blowup of the solution and also the finiteness of type II blowup points. These results extend some facts on the Smoluchowski-Poisson equation associated with the Boltzmann entropy in two space dimensions and actually, we use mass quantization of the blowup family of stationary solutions for the proof. In this first paper, we show local in time existence of the weak solution. Adv. Differential Equations, Volume 14, Number 5/6 (2009), 433-476. First available in Project Euclid: 18 December 2012 Permanent link to this document Mathematical Reviews number (MathSciNet) Zentralblatt MATH identifier Suzuki a, Takashi; Takahashi, Ryo. Degenerate parabolic equation with critical exponent derived from the kinetic theory, I, generation of the weak solution. Adv. Differential Equations 14 (2009), no. 5/6, 433--476. https://projecteuclid.org/euclid.ade/1355867256

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https://beautyofnutrition.com/packs/

math

Save Big with our most popular packs! $94 Loyal Customer Price $157 Retail Price Metabolic Burn- Chocolate or Vanilla$119 Loyal Customer Price $199 Retail Price It Works System$147 Loyal Customer price $245 Retail Price $112 Loyal Customer PRice $189 Retail Price It Pack-berry or orange $179 Loyal customer price $299 Retail Price *These statements have not been evaluated by the Food and Drug Administration. These products are not intended to diagnose, treat, cure or prevent any disease.

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http://www.shmoop.com/series/divergence-test-exercises-3.html

math

Use only the Divergence Test to determine if the statement is true, false, or can't be decided yet. The series might converge. For the series, look at the limit of the terms. If the series diverges. If there's hope the series might converge, but we can't tell when our only tool is the Divergence Test. Since 0.9 is less than 1, This means the statement " might converge"

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https://waseda.elsevierpure.com/ja/publications/weak-addition-invariance-and-axiomatization-of-the-weighted-shapl

math

In this paper, we give a new axiomatization of the weighted Shapley value. We investigate the asymmetric property of the value by focusing on the invariance of payoff after the change in the worths of singleton coalitions. We show that if the worths change by the same amount, then the Shapley value is invariant. On the other hand, if the worths change with multiplying by a positive weight, then the weighted Shapley value with the positive weight is invariant. Based on the invariance, we formulate a new axiom, $$\omega $$ω-Weak Addition Invariance. We prove that the weighted Shapley value is the unique solution function which satisfies $$\omega $$ω-Weak Addition Invariance and Dummy Player Property. In the proof, we introduce a new basis of the set of all games. The basis has two properties. First, when we express a game by a linear combination of the basis, coefficients coincide with the weighted Shapley value. Second, the basis induces the null space of the weighted Shapley value. By generalizing the new axiomatization, we also axiomatize the family of weighted Shapley values. ASJC Scopus subject areas

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https://boruxaxofid.stylehairmakeupms.com/how-to-write-a-formula-in-excel-for-percentages-1066eq.html

math

You probably already know that multiplying a decimal by turns it into a percentage. If you need a more sophisticated formula for solving a percentage problem, or if you want troubleshooting advice, the best thing to do is ask a question in the Excel forum on the Microsoft Answers site. Highlight the cell with the first number, then enter the "-" symbol. In this case, you can use the SUMIF function to add up all numbers relating to a given product first, and then divide that number by the total, like this: In an empty cell, enter one of the below formulas: A large range of cells Click the first cell in the range, and then hold down Shift while you click the last cell in the range. To increase an amount by a percentage, use this formula: This is useful when you want to type just a single percentage on your worksheet, such as a tax or commission rate. Keep this in mind if you want to change this column to percentage format. The question is - how much do you have to pay on top of the net price. The next example is slightly more complicated. Nonadjacent rows or columns Click the column or row heading of the first row or column in your selection; then hold down Ctrl while you click the column or row headings of other rows or columns that you want to add to the selection. You cannot cancel the selection of a cell or range of cells in a nonadjacent selection without canceling the entire selection. In cell B1 you could write: On a simpler level, the first thing to know is that a…ll formulas must start with the equals sign. Tip If you are completing a one-time calculation, write the formula as an absolute reference. Adjacent rows or columns Drag across the row or column headings. Suppose, you have the number of "Ordered items" in column B and "Delivered items" in column C. Calculating percentage of total in Excel In fact, the above example is a particular case of calculating percentages of a total. How do you write formulas for Excel. This is how you calculate percentage in Excel. Remember to increase the number of decimal places if needed, as explained in Percentage tips. Select the per cent cell and choose your format. In a column beside that,you would have your FREQUENCY function to calculate the amount foreach week, based on the source data from the set of week numbersthat you have calculate. The format should resemble the following: The mathematical formula for calculating percentages is the amount divided by the total. Calculating percent change between 2 columns Suppose that you have the last month prices in column B and this month prices in column C. The dollar sign fixes the reference to a given cell, so that it never changes no matter where the formula is copied. Parts of the total are in multiple rows In the above example, suppose you have several rows for the same product and you want to know what part of the total is made by all orders of that particular product. Considering the above, our Excel formula for percentage change takes the following shape: Kasper Langmann, Co-founder of Spreadsheeto Now, as you can see, you have the percentage change in decimal format. How to write percentage formulas in Excel Grant D. In this case, you can use the SUMIF function to add up all numbers relating to a given product first, and then divide that number by the total, like this: So if you wanted to find what percentage 53 is of 92 then you would use the following formula:. Aug 02, · Calculating percentages. As with any formula in Excel, you need to start by typing an equal sign (=) in the cell where you want your result, followed by the rest of the formula. So, I hear your next question in my head — which formula do I use to get the result I desire? Well, that depends. How to I write an IF statement that if I divide two negative numbers, the results show a negative percentage and not a positive percentage? You can format negative numbers to display with parentheses, but putting numbers in parentheses in an excel formula doesn't treat it as a negative. For instance, % = as the only. Percentages in Excel are stored as decimal values. For example, 25% is stored as the value50% is stored as the valueetc. It is the formatting of a cell that makes the underlying decimal value appear as. On the Formula Ribbon (Excel ), in the Formula Auditing section, click on the Show Formulas button. You will see both labels and formulas, instead of values in the cells. How to calculate percentage in Excel - formula examples by Svetlana Cheusheva | updated on June 28, Comments In this tutorial, you will lean a quick way to calculate percentages in Excel, find the basic percentage formula and a few more formulas for calculating percentage increase, percent of total and more. 1. Input Initial Data in Excel. Input the data as follows (or start with the download file "stylehairmakeupms.com" contained in the tutorial source files). This worksheet is for Expenses. Later in this tutorial, we’ll use the Grades worksheet.How to write a formula in excel for percentages

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https://www.swimo.de/en/service/cnc-3d/

math

Our milling machine is a 3-axis CNC milling machine, i.e. the model can only be approached from one side at a time. A bangle is milled from 2 sides, so an undercut model is not possible. Many materials can be milled, such as wood, horn, wax, various plastics, HPL, GRP, CFRP, etc. Unfortunately, metals are not possible except for aluminium and automatic steel. here are a few impressions:

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https://cl.desmos.com/t/can-i-hide-the-action-button-until-points-are-moved-on-a-graph/4097

math

I have a slide where I want students to translate a triangle. I want students to work on the graph and drag the points to where the image should be. I have created an action button that reveals the image but I would like it to appear after the student moves the points. If this is possible, I would really appreciate some help. You could have it hidden when the coordinates of the point are equal to the original coordinates. So if the point starts at the origin for example have hidden: graph.number(xCord) = 0 and graph.number(yCord) = 0 Thank you very much, I think that is a great idea but I could not get it to work. I get a message “Parameters to sinks and sources must be constant.” Change xCord and yCord to whatever your variable names are and put them in backticks: hidden: graph.number(`x_1`)=0 and graph.number(`y_1`)=0 Without backticks or quotes, it thinks you’re trying to input variable text, rather than the actual name of the variable from the graph. Thanks for clarifying - sorry for being ambiguous! Thank you both very much,

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https://atozchemistry.com/what-is-definition-of-1-mole/

math

Answer here ! Top Answer by best Chemistry Teacher in patna , IITian Rishi Sir Definition of 1 mole by best chemistry teacher in patna, IITian Rishi Sir A mole is the amount of a substance that contains as many entities (atoms, molecules or other particles) as there are atoms in exactly 0.012 kg (or 12 g) of the carbon-12 isotope. From mass spectrometer we found that there are 6.023 × 1023 atoms present in 12 g of C-12 isotope. The number of entities in 1 mol is so important that it is given a separate name and symbol known as Avogadro constant denoted by NA. i.e. on the whole we can say that 1 mole is the collection of 6.02 × 1023 entities. Here entities may represent atoms, ions, molecules or even pens, chair, paper etc also include in this but as this number (NA) is very large therefore it is used only for very small things.

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http://www.maths9.com/practice/Sixth-Grade/Ratios-and-Proportions/Ratio-between-two-quantities-having-similar-or-different-units-word-problems

math

Practice Maths - Maths9.com Practice Score out of 100 - Practice >> - Sixth Grade - Ratios and Proportions: Ratio between two quantities having similar or different units – word problems Ronald buys a geyser for $ 3680 and sells it for $ 3950. Find the ratio of the cost price of the geyser to the selling price of the geyser.

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https://brokerezkhe.netlify.app/griswold71019lo/investment-terms-alpha-and-beta-230

math

23 Apr 2013 volatility was heading lower right into the financial crisis.” Beta may not be predictive on the risk front. But there are also problems on the return Alpha is used in conjunction with Beta, which measures the market's overall volatility or risk, known as systematic market risk. Excess returns of an investment , 30 Nov 2005 It is the opposite of beta, the term applied to investments whose returns tend to track the market. With conventional beta investments in stocks The alpha of portfolio i for a certain time span represents the return of the portfolio above (or. 2. Beta is not simply an asset's return volatility relative to market Alpha may be a common investment term, but it remains commonly Fund B had a lower excess return than Fund A, but the manager took far less risk (a beta of Market volatility had been so low for so long that taking short positions in the CBOE VIX index—a volatility indicator—became an enormously crowded trade. 14 Jun 2018 The risk-adjusted RevPAR measure is designed to determine whether a hotel market or segment's RevPAR growth compensates for its volatility. Redefining the art of investing from striving for positive alpha to avoiding negative alpha. October 2018 Harder-to-capture types of beta require more skill than easily-captured types of beta. alpha. And this is not just a matter of terminology. 11 Nov 2014 Alpha! It's a term frequently used within the managed futures space, but risk- reward profile of an investment: alpha, beta, standard deviation, 17 Apr 2016 The beta anomaly—negative (positive) alpha on stocks with high (low) beta— arises from beta's positive correlation with idiosyncratic volatility 6 Dec 2013 It's frustrating for advisors to find ways to add value when investment advice and products are increasingly commoditized. But this supposes - A - Alpha - The amount of return expected from an investment from its inherent value. Alternative Minimum Tax (AMT) - Federal tax, revamped by the Tax Reform Act of 1986, aimed at ensuring that wealthy individuals, trusts, estates and corporations pay at least some tax. The Sharpe Ratio can help investors compare investments in terms of both risks Beta coefficients can be used to calculate an investment's alpha, which is a 11 Jul 2017 Next up: Beta (β) measures how closely a stock moves relative to the index. To understand Beta, let's look at the volatility in the price of a stock. For any given portfolio, investment decisions generally financial economics, it is sometimes used as simple terms as alpha and beta because the objective Investing in Alpha vs Beta. “Beta” is a coefficient that reflects the volatility, or systematic risk, of an There are five main indicators of investment risk that apply to the analysis of stocks, bonds and mutual fund portfolios. They are alpha, beta, r-squared, standard deviation and the Sharpe ratio Two common terms that I see used a lot are Alpha and Beta. Their definitions are below. Alpha A mathematical estimate of the amount of return expected from an investment's inherent values. It measures the difference between a stock's actual performance and the performance anticipated in light of the stock's risk and the behavior of the market. Alpha measure's a stock's risk adjusted performance. Alpha is a measure of the difference between a portfolio's actual returns and its expected performance, given its level of risk as measured by beta. For example, if a mutual fund returned 10% in a year in which the S&P 500 rose only 5%, that fund would have a higher alpha. Beta definition - What is meant by the term Beta ? meaning of IPO, Definition of Beta on The Economic Times. Also see: volatility, CAPM, NSE Nifty, alpha. 12 Jul 2019 Alpha is the excess return on an investment relative to the return on a benchmark index. Beta is the measure of relative volatility. Alpha and beta Beta is a historical measure of volatility. Beta measures how an asset (i.e. a stock, an ETF, or portfolio) moves versus a benchmark (i.e. an index). Alpha is a 2 Mar 2018 These terms refer to two important investing concepts. In simple English, "alpha" refers to how well an investment performed relative to a certain REIT Volatility, Correlation, Beta, and Alpha as of Mid-2017: Not Your Father's Small-Cap Value Stocks (Thank Goodness). 8/22/2017 | By Brad Case. Share:. 9 Oct 2012 So how does a sponsor work with beta, alpha, and investment upside exposure while limiting downside risk and overall portfolio volatility. Hedging on Hedge Funds (postscript on correlations, beta, and “alpha”). May 16, 2016 - Cliff Asness. Topics - Alternative Investing Hedge Funds. Hedging on Alpha is the excess return on an investment relative to the return on a benchmark index. Beta is the measure of relative volatility. Alpha and beta are both risk ratios that calculate, compare

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CC-MAIN-2024-18

https://www.education.com/lesson-plan/i-got-the-power/

math

Do your students understand the power of 10? This lesson will allow your students to see the utility of the power of 10 in mathematics and come to a concrete conclusion of how 10 impacts the value of mathematical equations. Students will be able to identify and explain patterns in the number of zeros of the product when multiplying a number by powers of 10, identify and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10 and use whole number exponents to denote powers of 10. Review place value and order of operations. Remind students that our number system is a decimal system and it relies on groupings of 10s. Tell students that we also utilize a place value system, with the value of each digit depending on its position or place in the number. Write "1,000,000" on the board and ask students to identify at least one other way this number can be written. Possible answers include: writing the words “one million” or 10 x 10 x 10 x 10 x 10 x 10. Tell students that mathematicians created a shortcut for writing very large numbers, and that today they are going to explore this technique.

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CC-MAIN-2022-40

https://math.answers.com/Q/What_are_the_different_classification_of_algebraic_expression_according_to_the_number_of_term

math

An algebraic equation contains an equality sign whereas an algebraic expression has no equality sign When the value of a variable in an algebraic expression changes, the value of the expression can change. An algebraic expression is a collection of different terms that does not include an equality sign Terms with different powers of the variable. An algebraic expression includes one or more variables (x, y, a, b) that can have more than one value, especially with regard to each other when there are two or more. different classification of hotel according to department of tourism X2 Is an algebraic expression. X2 = 4 Is an equation that can be solved for X. The variable, X, in this case, has two values. In the expression any value can be substituted for X. Each term in an algebraic expression is separated by plus & minus 5x + 4 = 12x has two different terms (5x, 4). Good answer. Actually the equation has three terms, 5x, 4 and 12x. x/5 + y/3 A polynomial is a function or expression that has two or more algebraic terms. Usually, each term has a different exponential power. Usually they are opposite processes. Factorisation is taking an algebraic expression and partitioning it into factors in brackets (or parentheses). Expansion is taking such brackets and multiplying them out to a simple - if lengthy - expression. (n-4)/5 Remember p.e.m.d.a.s. The parentheses signify which part of the expression to do first. They are very important. You get a different answer without them.

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CC-MAIN-2022-21

http://www.oogazone.com/2017/best-free-linear-graph-3d-vector-library/

math

Calculator to use for variety of purposes, including the production of d, and d euclidean, and polar graphs.Vector has both magnitude and direction. we use vectors to, for example, describe the velocity of moving objects. in this , you'll learn how to write and draw . [top] convert_unordered_to_ordered this function takes graph, defined by vector of sample_pair objects and converts it into the equivat graph . Graphing. with over builtin graph types, origin makes it easy to create and customize publicationquality graphs. you can simply start with builtin graph . When posted about decals last week, number of readers commented that they would be interested in posts about linear algebra as it applies to game development. . Online d and d plotter with root and intersection finding, easy scrolling, and exporting features. Dlib contains wide range of machine learning algorithms. all designed to be highly modular, quick to execute, and simple to use via clean and . Learn linear algebra for freevectors, matrices, transformations, and more. Grapher is computer program bundled with os (now called macos) since version .that is able to create d and d graphs from simple and complex equations. Threedimensional e (also e or, rarely, tridimensional e) is geometric setting in which three values (called parameters) are required to determine . Welcome to ixl'precalculus page. practice math online with unlimited questions in more than precalculus math skills. Api reference this is the cl and function reference of scikitlearn. please refer to the full user guide for further details, as the cl and function raw .

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CC-MAIN-2018-13

https://matheducators.stackexchange.com/questions/17320/in-preparation-for-exams-question-bank-or-questions-with-omitted-particulars

math

I have been doing a little bit of experimenting when it comes time to review with the class in preparation for the final exam. The last handout I have been giving my students has usually been a compilation of problems similar to the ones they have been accustomed to seeing throughout the course. Through the use of textbooks, I can save some time by not having to come up with the questions myself, but the textbooks sometimes do not use the same language that I use in class or on prior written assignments. Recently, I have been considering the option of either: A) a list of twenty-five possible questions, out of which eight to ten will be on the final exam, or B) the exact eight to ten questions that will be on the final exam, with the particulars blacked out (particulars being numbers, equations, functions, etc.). Benefits of A: - allows students to strengthen all core skills required to say that they have a satisfactory understanding of all course material - if all twenty-five questions are completed to perfection, the student should have no problem reiterating the solution come exam day (barring test anxiety, time management problems, and other factors) - hedging bets (we all know this problem when we studied stats): what is the minimum number of questions I should be completely clear on how to do if I want to have a good chance of scoring at least an $80\%$, etc. Benefits of B: - allows students to focus solely on the exact type of question they should expect - gives students the opportunity to predict how much time should be spent for each question, and, by extension, how much time can be spent studying for each topic To current students: if you were given the option, which would you prefer? Can you think of other ways that each option can benefit you? To teachers: which option have you personally used with your students before? If neither, do you see yourself employing either of these methods when it comes to exam preparation for your students?

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https://www.acmicpc.net/problem/6125

math

|시간 제한||메모리 제한||제출||정답||맞힌 사람||정답 비율| |1 초||128 MB||83||56||52||74.286%| Bessie's grandfather was a pirate who accumulated a great treasure chest of golden plunder. He hid the treasure chest in a cave that Bessie has recently discovered right on Farmer John's land! Just inside the cave's entrance she found a map that told her how to get the treasure. The cave has P passages (3 <= P <= 5,000) conveniently numbered 1..P. The entrance is passage 1; the treasure is located in some reachable passage T (2 <= T <= P), whose value is supplied. Passages are all approximately the same length; each one leads to a split where hitherto unexplored numbered passages take the inquisitive cow deeper underground. No passage appears as the split from more than one passage, and the map contains a total of NS splits (1 <= NS <= 5,000). Bessie wants to know both how far away from the entrance the treasure lies and also which passage numbers to take to get to the treasure. Consider the schematic representation of a cave shown below. Passage numbers are shown close to the passage they name. For this example, the treasure is at the end of passage number 7: 3/ / + / \ /5 2/ 4\ / 1 / + ----+ 6\ #7 /11 \ \ / / 13\ + + 8\ 10/ \ \ / \12 + 9\ \ Bessie would have to traverse passages 1, 2, 4, 6, and 7 to get to the treasure, a total distance of 5 (which is simply the passage count). The input file includes a set of lines, each with a passage number N (1 <= N <= P) and the two passages (B1 and B2; 1 <= B1 <= P; 1 <= B2 <= P) that branch off from it. Some line in the input file will include passage number 1 and its two branches (for our example, passages 2 and 13; likewise, passage number 8 has two branches: 9 and 10). Tell Bessie how to get to the treasure. 13 6 7 6 7 8 2 3 4 10 11 12 8 9 10 1 2 13 4 5 6 5 1 2 4 6 7

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CC-MAIN-2023-40

http://www.mywordsolution.com/question/objectve-questions-on-bond-valuation-suppose/916772

math

problem1. Suppose that all interest rates in the economy decline from 10 percent to 9 percent. Determine the largest percentage increase in price? [A] A 10-year bond with a 10% coupon. [B] A 10-year zero coupon bond. [C] An 8-year bond with a 9% coupon. [D] A 1-year bond with a 15% coupon. [E] A 3-year bond with a 10% coupon. problem2. Determine the greatest interest rate price risk? [A] A 10-year, $1,000 face value, 10% coupon bond with semiannual interest payments. [B] A 10-year $100 annuity. [C] A 10-year, $1,000 face value, zero coupon bond. [D] A 10-year, $1,000 face value, 10% coupon bond with annual interest payments. [E] All 10-year bonds have the same price risk since they have the same maturity. problem3. Find the correct statements? [A] Risk refers to the chance that some unfavorable event will occur, and a probability distribution is completely described by a listing of the likelihood of unfavorable events. [B] A stock with a beta of -1.0 has zero market risk if held in a 1-stock portfolio. [C] The SML relates its required return to a firm's market risk. The slope and intercept of this line cannot be controlled by the financial manager. [D] Portfolio diversification reduces the variability of returns on an individual stock. [E] When company-specific risk has been diversified away, the inherent risk that remains is market risk, which is constant for all stocks in the market.

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CC-MAIN-2017-17

https://www.hindawi.com/journals/aaa/2012/548292/

math

Advanced Theoretical and Applied Studies of Fractional Differential EquationsView this Special Issue Research Article | Open Access Ibrahim Karatay, Serife R. Bayramoglu, "A Characteristic Difference Scheme for Time-Fractional Heat Equations Based on the Crank-Nicholson Difference Schemes", Abstract and Applied Analysis, vol. 2012, Article ID 548292, 11 pages, 2012. https://doi.org/10.1155/2012/548292 A Characteristic Difference Scheme for Time-Fractional Heat Equations Based on the Crank-Nicholson Difference Schemes We consider the numerical solution of a time-fractional heat equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with Riemann-Liouville fractional derivative of order α, where . The main purpose of this work is to extend the idea on Crank-Nicholson method to the time-fractional heat equations. We prove that the proposed method is unconditionally stable, and the numerical solution converges to the exact one with the order . Numerical experiments are carried out to support the theoretical claims. Fractional calculus is one of the most popular subjects in many scientific areas for decades. Many problems in applied science, physics and engineering are modeled mathematically by the fractional partial differential equations (FPDEs). We can see these models adoption in viscoelasticity [1, 2], finance [3, 4], hydrology [5, 6], engineering [7, 8], and control systems [9–11]. FPDEs may be investigated into two fundamental types: time-fractional differential equations and space-fractional differential equations. Several different methods have been used for solving FPDEs. For the analytical solutions to problems, some methods have been proposed: the variational iteration method [12, 13], the Adomian decomposition method [13–16], as well as the Laplace transform and Fourier transform methods [17, 18]. On the other hand, numerical methods which based on a finite-difference approximation to the fractional derivative, for solving FDPEs [19–24], have been proposed. A practical numerical method for solving multidimensional fractional partial differential equations, using a variation on the classical alternating-directions implicit (ADI) Euler method, is presented in . Many finite-difference approximations for the FPDEs are only first-order accurate. Some second-order accurate numerical approximations for the space-fractional differential equations were presented in [26–28]. Here, we propose a Crank-Nicholson-type method for time-fractional differential heat equations with the accuracy of order . In this work, we consider the following time-fractional heat equation: Here, the term denotes -order-modified Riemann-Liouville fractional derivative given with the formula: where is the Gamma function. Remark 1.1. If , then the Riemann-Liouville and the modified Riemann-Liouville fractional derivatives are identical, since the Riemann-Liouville derivative is given by the following formula: If is nonzero, then there are some problems about the existence of the solutions for the heat equation (1.1). To rectify the situation, two main approaches can be used: the modified Riemann-Liouville fractional derivative can be used or the initial condition should be modified . We chose the first approach in our work. 2. Discretization of the Problem In this section, we introduce the basic ideas for the numerical solution of the time-fractional heat equation (1.1) by Crank-Nicholson difference scheme. For some positive integers and , the grid sizes in space and time for the finite-difference algorithm are defined by and , respectively. The grid points in the space interval are the numbers , , and the grid points in the time interval are labeled , . The values of the functions and at the grid points are denoted and , respectively. As in the classical Crank-Nicholson difference scheme, we will obtain a discrete approximation to the fractional derivative at . Let Then, we have Now, we will find the approximations for and : where Similarly, we can obtain where and Then, we can write the following approximation: where On the other hand, using the mean-value theorem, we get where and . So, we obtain the following second-order approximation for the modified Riemann-Liouville derivative: 3. Crank-Nicholson Difference Scheme Using the approximation above, we obtain the following difference scheme which is accurate of order : We can arrange the system above to obtain The difference scheme above can be written in matrix form: where , , , , , and . Here, and are the matrices of the form We note that the unspecified entries are zero at the matrices above. Using the idea on the modified Gauss-Elimination method, we can convert (3.3) into the following form: Now, we need to determine the matrices and satisfying the last equality. Since , we can select and . Combining the equalities and and the matrix equation (3.3), we have Then, we write where . So, we obtain the following pair of formulas: where . 4. Stability of the Method The stability analysis is done by using the analysis of the eigenvalues of the iteration matrix () of the scheme (3.5). Let denote the spectral radius of a matrix , that is, the maximum of the absolute value of the eigenvalues of the matrix . We will prove that , (), by induction. Since is a zero matrix . Moreover, , since is of the form therefore, . Now, assume . After some calculations, we find that and we already know that and for : Since , it follows that . So, for any , where . Remark 4.1. The convergence of the method follows from the Lax equivalence theorem because of the stability and consistency of the proposed scheme. 5. Numerical Analysis Example 5.1. Consider Exact solution of this problem is . The solution by the Crank-Nicholson scheme is given in Figure 1. The errors when solving this problem are listed in the Table 1 for various values of time and space nodes. The errors in the table are calculated by the formula and the error rate formula is . Example 5.2. Consider Exact solution of this problem is . The solution by the Crank-Nicholson scheme is given in Figure 2. The errors when solving this problem are listed in Table 2 for various values of time and space nodes and several values of . It can be concluded from the tables and the figures that when the step size is reduced by a factor of 1/2, the error decreases by about 1/4. The numerical results support the claim about the order of the convergence. In this work, the Crank-Nicholson difference scheme was successfully extended to solve the time-fractional heat equations. A second-order approximation for the Riemann-Liouville fractional derivative is obtained. It is proven that the time-fractional Crank-Nicholson difference scheme is unconditionally stable and convergent. Numerical results are in good agreement with the theoretical results. - X. Li, X. Han, and X. Wang, “Numerical modeling of viscoelastic flows using equal low-order finite elements,” Computer Methods in Applied Mechanics and Engineering, vol. 199, no. 9–12, pp. 570–581, 2010. - R. L. Bagley and P. J. Torvik, “Theoretical basis for the application of fractional calculus to viscoelasticity,” Journal of Rheology, vol. 27, no. 3, pp. 201–210, 1983. - M. Raberto, E. Scalas, and F. Mainardi, “Waiting-times and returns in high-frequency financial data: an empirical study,” Physica A, vol. 314, no. 1–4, pp. 749–755, 2002. - E. Scalas, R. Gorenflo, and F. Mainardi, “Fractional calculus and continuous-time finance,” Physica A, vol. 284, no. 1–4, pp. 376–384, 2000. - D. A. Benson, S. W. Wheatcraft, and M. M. Meerschaert, “Application of a fractional advection-dispersion equation,” Water Resources Research, vol. 36, no. 6, pp. 1403–1412, 2000. - L. Galue, S. L. Kalla, and B. N. Al-Saqabi, “Fractional extensions of the temperature field problems in oil strata,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 35–44, 2007. - I. Podlubny, Fractional Differential Equations: An introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. - X. Li, M. Xu, and X. Jiang, “Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition,” Applied Mathematics and Computation, vol. 208, no. 2, pp. 434–439, 2009. - J. A. T. Machado, “Discrete-time fractional-order controllers,” Fractional Calculus & Applied Analysis, vol. 4, no. 1, pp. 47–66, 2001. - O. P. Agrawal, O. Defterli, and D. Baleanu, “Fractional optimal control problems with several state and control variables,” Journal of Vibration and Control, vol. 16, no. 13, pp. 1967–1976, 2010. - D. Baleanu, O. Defterli, and O. P. Agrawal, “A central difference numerical scheme for fractional optimal control problems,” Journal of Vibration and Control, vol. 15, no. 4, pp. 583–597, 2009. - Z. M. Odibat and S. Momani, “Application of variational iteration method to nonlinear differential equations of fractional order,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 27–34, 2006. - Z. Odibat and S. Momani, “Numerical methods for nonlinear partial differential equations of fractional order,” Applied Mathematical Modelling, vol. 32, no. 1, pp. 28–39, 2008. - S. Momani and Z. Odibat, “Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 488–494, 2006. - Z. M. Odibat and S. Momani, “Approximate solutions for boundary value problems of time-fractional wave equation,” Applied Mathematics and Computation, vol. 181, no. 1, pp. 767–774, 2006. - S. S. Ray and R. K. Bera, “Analytical solution of a fractional diffusion equation by Adomian decomposition method,” Applied Mathematics and Computation, vol. 174, no. 1, pp. 329–336, 2006. - I. Podlubny, The Laplace Transform Method for Linear Differential Equations of Fractional Order, Slovac Academy of Science, Bratislava, Slovakia, 1994. - B. Baeumer, D. A. Benson, and M. M. Meerschaert, “Advection and dispersion in time and space,” Physica A, vol. 350, no. 2–4, pp. 245–262, 2005. - Z. Q. Deng, V. P. Singh, and L. Bengtsson, “Numerical solution of fractional advection-dispersion equation,” Journal of Hydraulic Engineering, vol. 130, no. 5, pp. 422–431, 2004. - V. E. Lynch, B. A. Carreras, D. del-Castillo-Negrete, K. M. Ferreira-Mejias, and H. R. Hicks, “Numerical methods for the solution of partial differential equations of fractional order,” Journal of Computational Physics, vol. 192, no. 2, pp. 406–421, 2003. - M. M. Meerschaert and C. Tadjeran, “Finite difference approximations for two-sided space-fractional partial differential equations,” Applied Numerical Mathematics, vol. 56, no. 1, pp. 80–90, 2006. - M. M. Meerschaert and C. Tadjeran, “Finite difference approximations for fractional advection-dispersion flow equations,” Journal of Computational and Applied Mathematics, vol. 172, no. 1, pp. 65–77, 2004. - I. Karatay, S. R. Bayramoğlu, and A. Şahin, “Implicit difference approximation for the time fractional heat equation with the nonlocal condition,” Applied Numerical Mathematics, vol. 61, no. 12, pp. 1281–1288, 2011. - D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus: Models and Numerical Methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific Publishing, Hackensack, NJ, USA, 2012. - M. M. Meerschaert, H.-P. Scheffler, and C. Tadjeran, “Finite difference methods for two-dimensional fractional dispersion equation,” Journal of Computational Physics, vol. 211, no. 1, pp. 249–261, 2006. - C. Tadjeran, M. M. Meerschaert, and H.-P. Scheffler, “A second-order accurate numerical approximation for the fractional diffusion equation,” Journal of Computational Physics, vol. 213, no. 1, pp. 205–213, 2006. - L. Su, W. Wang, and Z. Yang, “Finite difference approximations for the fractional advection-diffusion equation,” Physics Letters A, vol. 373, no. 48, pp. 4405–4408, 2009. - A. M. Abu-Saman and A. M. Assaf, “Stability and convergence of Crank-Nicholson method for fractional advection dispersion equation,” Advances in Applied Mathematical Analysis, vol. 2, no. 2, pp. 117–125, 2007. - G. Jumarie, “Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results,” Computers & Mathematics with Applications, vol. 51, no. 9-10, pp. 1367–1376, 2006. - S. Zhang, “Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 5-6, pp. 2087–2093, 2009. - R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems, Interscience Publishers, New York, NY, USA, 1967. Copyright © 2012 Ibrahim Karatay and Serife R. Bayramoglu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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http://mathhelpforum.com/discrete-math/206465-time-logic-question.html

math

The clock in my lounge is 10 minutes slower than my wrist watch, which is 6 minutes slow. My tram always leaves 6 minutes early, although it is scheduled for 8:55am.It takes me 20 minutes to get to the tram stop. What time must I leave, according to my lounge clock, in order to catch my tram? E.None of these Correct Answer E Cos I should leave house at 8:29 but the lounge clock is 10 minutes slower so when it is 8:29 am it's actually 8:39 am.So I must leave house at 8:19 am instead? PS.I think the clock in the lounge will be 16 minutes overall i.e. 10 + 6 I must leave the house at 8:13 instead? Hope I am right?

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CC-MAIN-2017-13

https://pickwickbookshop.com/products/9780826471130

math

Learning Mathematics : Issues, Theory and Classroom Practice Author(s): Anthony Orton • Why do some students achieve more than others? • Do we have to wait until pupils are "ready"? • Can children discover math for themselves? • Does language interfere with the learning of math? This classic text, written from the viewpoint of the math teacher, provides answers to these and many more questions. Each chapter explores a particular issue that illustrates the interaction between theory and practice. New chapters have been included on cognition, pattern, and ICT.

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CC-MAIN-2023-06

https://www.arxiv-vanity.com/papers/1104.3296/

math

Quantum versus classical phase-locking transition in a driven-chirped oscillator Classical and quantum-mechanical phase locking transition in a nonlinear oscillator driven by a chirped frequency perturbation is discussed. Different limits are analyzed in terms of the dimensionless parameters and ( and being the driving amplitude, the frequency chirp rate, the nonlinearity parameter and the linear frequency of the oscillator). It is shown that for , the passage through the linear resonance for above a threshold yields classical autoresonance (AR) in the system, even when starting in a quantum ground state. In contrast, for , the transition involves quantum-mechanical energy ladder climbing (LC). The threshold for the phase-locking transition and its width in in both AR and LC limits are calculated. The theoretical results are tested by solving the Schrodinger equation in the energy basis and illustrated via the Wigner function in phase space. pacs:42.50.Hz, 42.50.Lc, 33.80.Wz, 05.45.Xt Autoresonance (AR) is a generic nonlinear phase-locking phenomenon in classical dynamics. It yields a robust approach to excitation and control of nonlinear oscillatory systems by a continuous self-adjustment of systems’ parameters to maintain the resonance with chirped frequency perturbations. Applications of AR exist in many fields of physics, examples being atomic and molecular systems Maeda 2007 ; Chelkowski , nonlinear optics Segev , Josephson junctions Ofer Naaman , hydrodynamics BenDavid , plasmas Danielson , nonlinear waves Lazar92 , and quantum wells Manfredi 2007 . Most recently, AR served as an essential element in the formation of trapped anti-hydrogen atoms at CERN ALPHA Nature ; ALPHA PRL and in studying the effect of fluctuations in driven Josephson junctions Kater . While the classical AR is well understood, the investigation of the quantum-mechanical limits of the problem has started only recently Gilad ; Manfredi 2007 ; Kater . The present study focuses on the interrelation between the classical and quantum descriptions of the autoresonant transition in the simplest case of a driven Duffing oscillator (modeling a driven diatomic molecule Zigler or a Josephson junction Ofer Naaman , for example) governed by the Hamiltonian where , is the chirped driving frequency and . We will assume that initially our oscillator is in a thermal equilibrium with the environment at temperature , but the chirped system’s response is sufficiently fast to neglect the effect of the environment on the out-of-equilibrium dynamics Kater . Classically, in autoresonance, after passage through the linear resonance at , the driven oscillator gradually self-adjusts its oscillation frequency to that of the drive by continuously increasing its energy Fajans , yielding a convenient control of the dynamics by variation of an external parameter (the driving frequency). The transition to the classical AR by passage through linear resonance has a threshold on the driving amplitude, scaling as Fajans . This threshold is sharp if the oscillator starts in its zero equilibrium, but in the presence of thermal noise it develops a width, scaling as PRL . Both the AR threshold and its width have their quantum-mechanical counterparts, which will be discussed in this work. When the problem of autoresonant transition is dealt with quantum-mechanically, two questions must be addressed. First, what are the differences between the classical and quantum evolutions of the chirped-driven nonlinear oscillator? In dealing with this question, Ref. Gilad suggested that the natural quantum-mechanical limit of the classical AR is a series of successive Landau-Zener (LZ) LZ transitions or energy ladder climbing (LC), where only two adjacent energy levels of the driven oscillator are coupled at any given time. In contrast, the classical AR behavior takes place when many levels are coupled at all times during the excitation Goggin . We will adopt and further develop this point of view here and describe different regimes in the problem in terms of two dimensionless parameters suggested in Gilad . These parameters are defined via the three physical time-scales in the system, i.e. the inverse Rabi frequency , the frequency sweep time scale , and the characteristic nonlinearity time scale (the time of passage through the nonlinear frequency shift between the first two transitions on the energy ladder). Then, by definition (this parameter measures the strength of the drive), and (a measure of the nonlinearity in the problem). We will show in this work that this parameter space describes all limiting cases of quantum-mechanical evolution in our system, including quantum initial conditions, the subsequent transition to either LC or AR, and the associated threshold phenomenon. Note, that have a meaning only in the case of a chirped system, because of the new time scale, , associated with this case. The second question, which must be addressed in the quantum-mechanical formulation of our problem is that of quantum fluctuations. As mentioned above, in the presence of thermal noise, the classical AR transition probability develops a width, scaling as with temperature PRL . Nevertheless, at very low temperatures, the quantum fluctuations should be taken into account. Recent experiments by Kater et al. Kater demonstrated quantum saturation of the width of the phase-locking transition in superconducting Josephson junctions at sufficiently low temperatures, confirming the prediction that in the classical width formula PRL should be replaced by an effective temperature, , where for high temperatures and saturates at at low temperatures. The experimental results imply that the fluctuations only determine the initial conditions of such a non-equilibrium oscillator and do not affect its time evolution. In this work, we will address the effect of quantum fluctuations in the AR problem theoretically and provide further justification of using the classical AR threshold width formula with replaced by . The scope of the paper will be as follows. In Sec. II we will use the quantum-mechanical energy basis in the rotating wave approximation and compare the driven dynamics of our oscillator in the quantum and classical regimes numerically. Section III will present the analytic description of the transition to phase-locking in terms of the parameter space in both classical AR and quantum LC regimes. In the same Section, the theory will be compared with numerical simulations. Section IV will focus on the effect of quantum fluctuations on the width of the phase-locking transition. Finally, we will address the phase space dynamics in the problem in Sec. V by solving the quantum Liouville equation for the Wigner function numerically and compare the phase space evolution with that in the energy basis. Our conclusions will be summarized in section VI. Ii Chirped dynamics in the energy basis We write the wave function of the oscillator governed by Eq.(1), , in the energy basis of the undriven () Hamiltonian (1). The associated Schrodinger equation yields where we approximate the energy levels Landau QM , , and . We assume a weak coupling, , and, consequently, neglect the nonlinear correction of order in the coupling term. Next, we define , where , substitute this definition into Eq. (4), and neglect the nonresonant terms (rotating wave approximation) to get where . Finally, we introduce , where and the dimensionless slow time , associated with the change of the driving phase due to the driving frequency chirp. Then Eq. (6) can be written as where , and , as defined in the Introduction. Note, that characterizes the strength of the coupling between the adjacent levels, while is associated with the nonlinearity in the problem and determines the degree of classicality in the system (see Sec. V). Note also that the rotating frame here is chirped instead of the usual, fixed frequency frame and, thus, there remains an explicit time dependence in Eq. (7). Our goal is to analyze these slow evolution equations, but first, we discuss different limits in the driven system in parameter space. The comparison between the classical AR and the quantum LC regimes was first discussed by Marcus et al. Gilad , who suggested the nonlinear resonance classicality criterion, , by requiring that the classical resonance width would include more than two quantum levels. Since the chirp rate cancels from this creterion, the latter characterizes the nonlinear resonance phenomenon in the system driven by constant frequency drive as well. The chirping introduces a new effect, i.e. a possibility of a continuous self-adjustment of the energy of the oscillator to stay in resonance with the drive. This yields a new condition, separating the classical AR and quantum LC transitions, where the dynamics of the chirped system is very different. In the LC transition, only two levels are coupled at a time and the system’s wave function climbs the energy ladder by successive LZ transitions LZ . For example, Eq. (7) yields the following two-level transformation matrix for the transition We can calculate the time of the transition, by equating the diagonal elements in this matrix, i.e. , so the time interval between two successive transitions is . On the other hand, the typical duration of each LZ transition has two distinct limits Finite LZ . In the non adiabatic (sudden) limit (), is of the order of unity, while in the opposite (adiabatic) limit, . Therefore, by comparing and , we expect to see well separated successive LZ steps, i.e. the LC, provided which describes both the sudden and the adiabatic limits. In contrast, the classical AR transition requires , which coincides with the nonlinear resonance classicality criterion mentioned above, when . In section V, a different argument will be suggested to explain why classical mechanics yields the correct description of the transition to autoresonance when a stronger inequality, , is satisfied, even when the system starts in the quantum mechanical ground state. Next, we discuss the numerical solutions of the problem and compare different regimes of chirped-driven dynamics. We have solved Eqs. (7) numerically, subject to ground state initial conditions at (the linear resonance corresponds to ). Each of the Figs. 1–3 corresponds to a different value of the nonlinearity parameter and show the distribution of the population of the levels in the system at four different times (subplots a-d). The subplots e-h in the Figures show the associated Wigner distributions (see Sec. V) at the same times. Figure 1 shows the case of the LC dynamics for and at , and (subplots a-d), and illustrates a clear time separation beyond the linear resonance between the successive LZ transitions. For example, we observe two groups of resonant and nonresonant levels at , separated by a valley centered at about . We find that the location of the resonant levels is determined by the slow time, i.e. , as shown above. Thus, the resonant (phase-locked) state in the system is efficiently controlled via the driving frequency and a given final state can be reached (and maintained) by terminating the frequency chirp at the desired energy level. We also see that there exists a single highly occupied level in the resonant group of levels at any given time, indicating successive LZ transitions, as expected in the LC regime. Our second numerical example is presented in Fig. 2 and illustrates the intermediate regime (as discussed above) with and , and (the subplots a-d). As in Fig. 1, a clear separation between the resonant and nonresonant groups of levels is seen in the Figure. We see that, typically, several levels are excited in the resonant group, but their number is small, so the driven dynamics can not be considered as classical. The last example (see Fig. 3) corresponds to the classical regime, , and . One observes a separation between resonant and nonresonant groups at . Note that in all our numerical examples about 50% only of the initial state is transferred to the continuing phase-locked state, leading to the question of resonant capture probability, which is discussed next. Iii Resonant capture probability iii.1 Threshold for phase-locking transitions For a given set we define the resonant capture probability, where is the number of the level separating the resonant and nonresonant groups of levels at sufficiently large times. For a given value of , the probability depends on the driving parameter, For example, in the case in Fig. 1, we use and the resonant capture probability is . Similarly, in the two examples in Figs. 2 and 3, we choose to get , respectively. We calculate the resonant capture probability by solving Eqs. (7) numerically subject to initial conditions, (the ground state), for different values of and . For a fixed , the capture probability is a monotonically increasing, smoothed step function of . We define the threshold for efficient phase-locking transition, , as the value of for 1/2 capture probability, i.e. . The full circles in Fig. 4 show for different values of . The dashed and dashed-dotted lines are the assymptotic theoretical predictions for the quantum LC and classical AR (see below), which agree with the results of our simulations in both limits. The line is the separator between the classical and the quantum regimes of the chirped nonlinear resonance, as discussed in Sec. II. This line crosses the threshold line at . One can see in the Figure that indeed, this point separates very different dependences of on associated with the quantum and classical dynamics of the chirped system. One can also see the oscillating pattern of the threshold at , where the transition to phase-locking involves a mixture of LC and multi-level LZ steps. Next, we calculate the threshold for phase-locking transitions analytically. iii.2 Quantum-mechanical ladder climbing In the quantum LC regime the nonlinearity parameter determines the time interval between successive resonances [see Eq. (8)]. In the case of a strong nonlinearity, at any given time only two levels are coupled, and the dynamics can be modeled by successive LZ transitions. In this case, we can calculate the probability of each transition separately, and multiply the probabilities. The two level transformation matrix (8) in the energy basis for the transition yields the transition probability via the LZ formula LZ where . We define the probability for capture into resonance in this case as the probability of occupying a sufficiently high energy level after successive LZ transitions, i.e. Then, solving , one finds the threshold for the LC transition, where for two digits accuracy we used in the rapidly converging product (11). Thus, the capture into resonance occurs in the first few LZ transitions and one can choose (see Fig. 1 in the definition Eq. (9) for calculating the capture probability near the threshold. This prediction is valid for large , as mentioned above. The dashed line in Fig. 4 represents Eq. (12), while the numerical result for 1/2 capture probability is shown by full circles. One can see a very good agreement between the two results in the LC limit (). However, in the intermediate regime (), oscillations in are observed before convergence at the predicted LC line. These oscillations are due to the mixing of more than two neighboring levels in passage through resonance (see Fig. 2). iii.3 Classical autoresonance As decreases, a growing number of levels are coupled simultaneously and the dynamics becomes increasingly classical. The classical AR phenomenon is now well understood Fajans . If one starts in the zero amplitude equilibrium, the autoresonant phase-locking is achieved for drives of amplitude above the critical value Fajans . When expressed in terms of , this classical threshold is translated into When thermal fluctuations are included, the transition probability develops a width scaling as with temperature PRL . At the same time, the threshold for 1/2 capture probability remains the same. Thus, in Eq. (13) is the classical counterpart of the quantum-mechanical observable in Eq. (12). This classical threshold is shown in Fig. 4 by dashed-dotted line, illustrating excellent agreement with simulations (full circles) in the classical regime, . It should be emphasized that the simulation results in the Figure are solutions of the quantum-mechanical equations (7) with parameters in the classical regime, while the probabilities of capture were calculated using the proper transition level for each value of , as defined in Eq. (9). In the next Section, we discuss the width of the autoresonant transition. Iv The width of the phase-locking transition Another observable of the phase-locking transition mentioned above is the width of the transition, which we define as the inverse slope of the phase-locking probability at . This width depends on the initial conditions governed by the thermal equilibrium with the environment. Classically, the thermal width of the autoresonant transition scales as PRL However, at very low temperatures, the classical thermal noise becomes negligible, but quantum fluctuations remain. Recent experiments in Josephson circuits Kater demonstrated quantum saturation of the transition width at the value obtained from Eq.(14), but with replaced by the energy of the ground level. More generally, it was suggested to calculate the width by replacing in the classical formula by an effective temperature, , in agreement with the experimental results. Using , we can translate Eq. (14) into the transition width in terms of in the zero temperature limit. The Josephson circuit experiments Kater were performed with , i.e. well inside the classical region (see Fig. 4). Interestingly, these experiments allowed to characterize the initial quantum ”temperature” of the system by measuring the final classical autoresonant state of the chirped excitation. We will justify this approach in the next Section by analyzing the dynamics of the associated Wigner function in phase space. In contrast to Eq. (15) valid when the final state of the system is classical , the threshold width of the phase-locking transition in the LC regime () can be calculated by evaluating the slope of from Eq. (11) at , yielding where we assume that the system is in the ground state initially. Figure 5 summarizes our theoretical predictions for the width of the phase-locking transition (for the same parameters as in Fig. 4) and compares them with those from numerical simulations via the Schrodinger equation (7). We see a good agreement in both the AR and LC limits, but notice significant oscillations of the width in the intermediate range of . Remarkably, while the thresholds in the classical and quantum-mechanical limits have very different scalings, the widths of the transitions are nearly the same. V Chirped dynamics in phase space Phase space dynamics comprises a convenient framework for comparison between classical and quantum evolution of the system. The Wigner function is one of the most useful phase space representations of the quantum mechanics, since it reduces to the classical phase space distribution in the limit of In this Section, we will study the dynamics of the Wigner function in our chirped oscillator problem in both the fixed and the rotating frames and discuss the transition to the classical limit in the problem. v.1 Wigner dynamics in the fixed frame The Wigner function associated with the Hamiltonian of form is governed by the quantum Liouville equation Schleich where and we neglect possible decay and decoherence processes. We take a low temperature limit, neglect the nonlinearity initially, and assume that the initial state of the system is in equilibrium with the environment, i.e. Schleich , where is the effective temperature. Note that at high temperatures, while at . In the case of interest the potential is a quartic [see Eq. (1)] and, therefore, only one term survives in the right hand side of (18), allowing to rewrite this equation in the following dimensionless form where, , , , , , and . In addition, we measure time in Eq. (20) in units of and introduce the dimensionless chirp rate . With this rescaling, the initial Wigner distribution (19) becomes . We solved Eq. (20) numerically with the same parameters as in the Schrodinger simulations and show the results in Figs. 1-3 (subplots e-h) at the same times for comparison. For a better representation of the Wigner distributions for different nonlinearities, we rescaled the axis in the Figures to , and . The dashed lines in the Figures are the separatrices, enclosing all bounded classical trajectories in phase space. We started all these simulations in the ground state, i.e. , at the initial time . Figure 1 compares the dynamics in phase space to that in the energy basis in the quantum LC regime , using the parameters , , and . The pattern seen near the origin in Fig. 1 is due to the quantum interference with a finite number of states in the nonresonant region. Figure 2 shows the intermediate case for parameters , , and . Finally, Fig. 3 corresponds to the classical AR case and the parameters , , and . As well known Zurek , in the near classical case the Wigner function becomes oscillatory on increasingly fast phase space scales. However, if coarse-grained (due to a finite numerical accuracy in our case), the Wigner function becomes almost everywhere positive as one approaches the classical distribution function, despite the initial quantum-mechanical ground state used in the simulations. The evolution of the Wigner function in the last example is nearly classical with the quantum signature entering only via the effective temperature of the initial state. In the classical formula (14) for the transition width, appears due to integration over the classical Maxwell-Boltzman distribution function (see PRL ). Therefore, for the quantum-mechanical initial conditions, we should integrate over the Wigner function in a thermal state instead over the classical distribution. But these two distributions have the same functional shape, except that is replaced by in Eq. (19). Therefore, as also confirmed in experiments Kater , one can use the classical formula for the threshold of the phase-locking transition at low temperatures, when starting from quantum-mechanical initial conditions. v.2 The dynamics in the rotating frame Here we further expand our discussion of the classical AR limit in our system via the Wigner representation in the rotating frame. The transformation to the rotating frame is accomplished using unitary transformation (see Dykman 2006 ) where the operator and is the driving phase [see Eq. (1)]. Then, by neglecting rapidly oscillating terms, the Hamiltonian (1) is transformed to The parameter in the last equation is familiar from the theory of the classical AR PRL , while is the dimensionless Plank constant, entering the commutation relation for the rescaled variables Here , , where and the dimensionless time associated with the dynamics governed by Hamiltonian (23) is . Next, we write the quantum Liouville equation in the rotating frame (see Ref. Dykman 2007 for similar developments for a constant frequency drive) where . The initial Wigner distribution (19) in the new variables is where . The left hand side of the Eq. (25) is identical to the Vlasov equation describing the evolution of a classical distribution of particles governed by Hamiltonian (23) without collisions and self-fields. Hence, as in the fixed frame, after coarse-graining the fast phase space oscillations of in the limit (), the dynamics in phase space can be treated classically Zurek . Therefore, both the threshold and the width of the autoresonant transition can be calculated from the classical theory as illustrated in Figs. 4 and 5, respectively, despite the quantum-mechanical initial conditions in the problem. In other words, is the measure of the classicality of the phase-locking transition in our chirped oscillator. Furthermore, in the limit of , only two parameters, and (via the initial conditions) fully characterize the AR transition. This result is in agreement with Eqs. (13) and (15) for the AR threshold and its width, where, remarkably, and enter separately. (a) We have studied the interrelation between the quantum-mechanical and classical dynamics of phase-locking transition in a Duffing oscillator driven by a chirped frequency oscillation. We studied the conditions for a continuous phase-locking in the driven system, such that the energy of the oscillator grows to stay in resonance with the varying driving frequency. The problem was defined by the temperature and three parameters, i.e. the driving amplitude the driving frequency chirp rate , and the parameter characterizing the nonlinearity of the oscillator. The nonlinearity in the problem was essential, since no persistent phase-locking in the system could be achieved for . (b) We have exploited a more natural representation of both the quantum-mechanical and classical dynamics in the problem via just two dimensionless parameters Gilad , and instead of , and . We have shown that describes the classicality of the phase-locking transition in the system, such that, for the system arrives at its classical autoresonant (AR) state after passage through linear resonance even when starting in the quantum-mechanical ground state. In contrast, for , the transition involves the energy ladder climbing (LC) process, i.e. a continuing sequence of separated Landau-Zener transitions between neighboring energy levels. The parameters have a meaning only in the case of a finite chirp rate, which introduces a new time scale, , in the problem. (c) The probability of transition to the phase-locked state versus has a characteristic -shape (a smoothed step function). The value of yielding 50% transition probability can be viewed as the threshold for the phase-locking transition. We have calculated this threshold and its width in both the quantum-mechanical LC and classical AR limits and compared the results to those from quantum-mechanical calculations starting in the ground state of the oscillator (see Figs. 4 and 5). We have found that, while in the LC limit the threshold is independent of , in the classical AR regime, the threshold is defined by the combination of parameters. The agreement of the theory and simulations in both limits was excellent, but characteristic oscillations of the threshold and the width were observed in the intermediate regime . (d) We have also studied the dynamics of the phase-locking transition in phase space by using the Wigner function representation, to explain the quantum saturation of the width of the threshold for AR transitions. The analysis of the Wigner (quantum Liouville) equation in the chirped rotating frame clarifies the role of as characterizing the degree of classicality in the phase-locking transition problem. (d) A possibility of engineering and control of a desired quantum state of the oscillator via ladder climbing process (see an example in Fig. 1) seems to be attractive in such applications as quantum computing. A generalization of this study to include possible decay, decoherence, and tunneling processes also seems to be important in future studies. Acknowledgements.This work was supported by the Israel Science Foundation under grant No. 451/10. - (1) H. Maeda, J. Nunkaew, and T.F. Gallagher, Phys. Rev. A 75, 053417 (2007). - (2) S. Chelkowski and A. Bandrauk, J. Chem. Phys. 99, 4279 (1993). - (3) A. Barak, Y. Lamhot, L. Friedland, and M. Segev, Phys. Rev. Lett. 103, 123901 (2009). - (4) O. Naaman, J. Aumentado, L. Friedland, J.S. Wurtele, and I. Siddiqi, Phys. Rev. Lett. 101, 117005 (2008). - (5) O. Ben-David, M. Assaf, J. Fineberg, and B. Meerson, Phys. Rev. Lett. 96, 154503 (2006). - (6) J.R. Danielson, T.R. Weber, and C.M. Surko, Phys. Plasmas 13, 123502 (2006). - (7) L. Friedland, Phys. Rev. Lett. 69, 1749 (1992). - (8) G. Manfredi and P.A. Hervieux, App. Phys. Lett. 91, 061108 (2007). - (9) G.B. Andresen et al. (ALPHA Collaboration), Nature (London) 468, 673 (2010). - (10) G.B. Andresen et al. (ALPHA Collaboration), Phys. Rev. Lett 106, 025002 (2011). - (11) K.W. Murch, R. Vijay, I. Barth, O. Naaman, J. Aumentado, L. Friedland, and I. Siddiqi, Nature Physics 7, 105 (2011). - (12) G. Marcus, L. Friedland, and A. Zigler, Phys. Rev. A 69, 013407 (2004). - (13) G. Marcus, A. Zigler, and L. Friedland, Europhys. Lett. 74, 43 (2006). - (14) J. Fajans and L. Friedland, Am. J. Phys. 69, 1096 (2001). - (15) I. Barth, L. Friedland, E. Sarid, and A.G. Shagalov, Phys. Rev. Lett. 103, 155001 (2009). - (16) L.D. Landau, Phys. Z. Sowjetunion 2, 46 (1932); C. Zener, Proc. R. Soc. London A137, 696 (1932). - (17) M.E. Goggin and P.W. Milonni, Phys. Rev. A 37, 796 (1988). - (18) L. Landau and E.M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory), 3rd ed. (Butterworth Heinemann, Oxford, 1977) p. 136. - (19) N.V. Vitanov and B.M. Garraway, Phys. Rev. A 53, 4288 (1996). - (20) W.P. Schleich, Quantum Optics in Phase Space, (Wiley-VCH Verlag, Berlin, 2001), Chap. 3.3, p.75. - (21) see, for example, W.H. Zurek, Rev. Mod. Phys. 75, 715 (2003). - (22) M. Marthaler and M.I. Dykman, Phys. Rev. A 73, 042108 (2006). - (23) M.I. Dykman, Phys. Rev. E 75, 011101 (2007).

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Instrument - Thermal Desorption Particle Beam Mass Spectrometer Thermal Desorption Particle Beam Mass Spectrometer What is being measured: Particle Chemical Composition Data recording software: Data analysis software: Manual Data Analysis Raw data time resolution: Analysis data averaging: Sensitivity to temperature (and correction method, if applicable): Sensitivity to relative humidity (and correction method, if applicable): Direct sampling of particles from chamber Sample preparation method: Sample residence time (chamber to instrument) (seconds): Length of tubing (cm): Instrument flow rate: 125 cm^3 min-1 Tubing inner diameter: Chemical identification method: Electron impact ionization fragmentation patterns. Data analysis method: Calibration drift estimate: Medium (on the order of days) Uncertainty estimation method: Uncertainty is estimated as +/- 30% for particle mass. Uncertainty arises from transport efficiency as a function of particle size and shape. Link to supplemental information: All measurements from this instrument have uncertainties of 20% of absolute value. All measurements from this instrument are normalized as a way to determine particle chemical composition.

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|Registration Deadline:||December 01, 2008 over 4 years ago| |To apply for Funding you must register by:||December 01, 2008 over 4 years ago| Collaborating to Teach Teachers: Mathematicians & Educators Team Up (PDF) Using Partnerships to Strengthen Elementary Mathematics Teacher Education, a 2-day workshop scheduled for December 11 & 12, 2008, is sponsored by the S. D. Bechtel, Jr. Foundation and the Mathematical Sciences Research Institute (MSRI) in Berkeley, CA. The workshop will explore the challenges to and benefits of a collaborative approach to the mathematical education of elementary teachers. A core problem perhaps the central problem for improving elementary school mathematics is the mathematical education of elementary teachers. The historic isolation of elementary teachers’ study of mathematics from their pedagogical preparation is increasingly seen to be both unnatural and ineffective. Indeed, the mathematical education of elementary teachers is inherently interdisciplinary as future teachers seek to gain the mathematical knowledge, the pedagogical knowledge and the knowledge of young students that is needed to become a successful mathematics teacher. Thus, it seems reasonable that an integrative learning approach to mathematical education of elementary teachers could yield substantial benefits. In part supported by the S. D. Bechtel, Jr. Foundation, mathematicians and educators at the University of Michigan, the University of Nebraska-Lincoln, Sonoma State University, and Mills College, have worked to form partnerships that meet the mathematical and pedagogical needs of their students. Faculty from these institutions who have participated in the Collaborative Teaching project will report on their efforts and lessons learned about working together to educate teachers of mathematics. These questions guide the workshop design: - What mathematical and pedagogical knowledge is of central importance to the preparation of elementary mathematics teachers? - How can courses and programs for elementary teachers be designed and structured so as to increase teachers’ mathematical knowledge for teaching? - What are the barriers, challenges and benefits to approaching the mathematical education of teachers as a partnership among mathematicians, educators, and master teachers? |Dec 11, 2008|| |Dec 12, 2008||

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What is the specific heat of oxygen (O2; M = 32.00 g/mol) at constant volume? How does it compare with specific heat for liquid water? Hint: Cv = 20.85 J/mol•K. 2.50 mol of an ideal monoatomic gas is placed in a constant volume container. How much heat should be supplied to raise the temperature of the gas by 44 K at temperatures close to room temperature? Calculate the heat absorbed by 1.4 moles of an ideal diatomic gas to increase its temperature by 38 K if it is placed in a constant volume container. Assume the process occurs at temperatures near room temperature.

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We use numbers everyday to count, to measure, to order and estimate and so on. Natural Numbers are positive numbers that we use to count and order. 0, 3, 6, 10, 204, 1000… In mathematical terminology, numbers used for counting are called “cardinal numbers” and numbers used for ordering are called “ordinal numbers“. TWO and SECOND, FIVE and FIFTH, THIRTY and THURTIES … Mathematicians use N to represent a set of all natural numbers. The set of natural numbers is an infinite set. This infinity is called countable infinity. Properties of Natural Numbers - 0 is a natural number (but some mathematicians do not include it in the list of natural numbers) - Every natural number has a number that comes after it and is also a natural number - 0 does not come after any natural number - If the number that comes after x is equal to the number that comes after y, then x = y Operations with Natural Numbers up to 1000 We can do several operations with natural numbers: order, compare, add, subtract, multiply and divide them. In this lesson you will learn how to add and subtract natural numbers up to 1000 by breaking the numbers down based on their place value. Place value of a digit is a very important concept. For example, 345 could be represented as a sum of 300 + 40 + 5. When adding it to another similar number, it often makes sense to add the components separately. Subtracting two natural numbers does not always result in a natural number. For example, 213 – 321 will produce a negative number, that is no longer a member of a set of natural numbers, but rather a negative integer. Place value of digits within a number is important when doing operations with natural numbers, as corresponding digits need to be added/subtracted respectively.

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https://pureportal.spbu.ru/en/publications/%D0%B8%D1%81%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5-%D1%83%D1%81%D1%82%D0%BE%D0%B9%D1%87%D0%B8%D0%B2%D0%BE%D1%81%D1%82%D0%B8-%D1%80%D0%B5%D1%88%D0%B5%D0%BD%D0%B8%D0%B9-%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D1%8F-%D0%BB%D1%8C%D0%B5%D0%BD%D0%B0%D1%80%D0%B0-%D1%81-%D1%80%D0%B0%D0%B7%D1%80%D1%8B%D0%B2%D0%BD%D1%8B%D0%BC%D0%B8-

math

A nonlinear mechanical system, whose dynamics is described by a vector ordinary differential equation of the Lienard type, is considered. It is assumed that the coefficients of the equation can switch from one set of constant values to another, and the total number of these sets is, in general, infinite. Thus, piecewise constant functions with infinite number of break points on the entire time axis, are used to set the coefficients of the equation. A method for constructing a discontinuous Lyapunov function is proposed, which is applied to obtain sufficient conditions of the asymptotic stability of the zero equilibrium position of the equation studied. The results found are generalized to the case of a nonstationary Lienard equation with discontinuous coefficients of a more general form. As an auxiliary result of the work, some methods for analyzing the question of sign-definiteness and approaches to obtaining estimates for algebraic expressions, that represent the sum of power-type terms with non-stationary coefficients, are developed. The key feature of the study is the absence of assumptions about the boundedness of these non-stationary coefficients or their separateness from zero. Some examples are given to illustrate the established results. |Translated title of the contribution||STABILITY ANALYSIS FOR THE LIENARD EQUATION WITH DISCONTINUOUS COEFFICIENTS| |Journal||ВЕСТНИК УДМУРТСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. КОМПЬЮТЕРНЫЕ НАУКИ| |State||Published - 2021| - nonlinear mechanical systems - Discontinuous coefficients - asymptotic stability - Lyapunov functions

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https://www.bloggalot.com/education-online-test-practice-for-class-9-mathematics

math

Category : Education where we know that number of student like doing study by online reason of they become more concentrate in online reading . because online study give opportunity to prepare all subject without face a problem . Online Test Practice For Class 9 Mathematics for best preparation of math .you must need of daily practice of math by which after some time you finds that every question answer of this subject you have known properly . so do the practice of math hole lesson by Well done! Your Request Forward Successfully!. Warning! Request already Forward Successfully!. Please select the category that most closely reflects your concern about the List, so that we can review it and determine whether it violates our Community Guidelines or isn't appropriate for all viewers. Abusing this feature is also a violation of the Community Guidelines, so don't do it.

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https://www.projecteuclid.org/journals/journal-of-symbolic-logic/volume-73/issue-4/Strictly-positive-measures-on-Boolean-algebras/10.2178/jsl/1230396929.short

math

We investigate strictly positive finitely additive measures on Boolean algebras and strictly positive Radon measures on compact zerodimensional spaces. The motivation is to find a combinatorial characterisation of Boolean algebras which carry a strictly positive finitely additive finite measure with some additional properties, such as separability or nonatomicity. A possible consistent characterisation for an algebra to carry a separable strictly positive measure was suggested by Talagrand in 1980, which is that the Stone space K of the algebra satisfies that its space M(K) of measures is weakly separable, equivalently that C(K) embeds into l∞. We show that there is a ZFC example of a Boolean algebra (so of a compact space) which satisfies this condition and does not support a separable strictly positive measure. However, we use this property as a tool in a proof which shows that under MA+\neg CH every atomless ccc Boolean algebra of size < 𝔠 carries a nonatomic strictly positive measure. Examples are given to show that this result does not hold in ZFC. Finally, we obtain a characterisation of Boolean algebras that carry a strictly positive nonatomic measure in terms of a chain condition, and we draw the conclusion that under MA+\neg CH every atomless ccc Boolean algebra satisfies this stronger chain condition. "Strictly positive measures on Boolean algebras." J. Symbolic Logic 73 (4) 1416 - 1432, December 2008. https://doi.org/10.2178/jsl/1230396929

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https://questions.llc/questions/1876489/how-many-terms-are-in-the-following-polynomial-y-4-7y-3

math

How many terms are in the following polynomial -y^4 +7y^3 well, terms are separated by + and - signs, so ... 2 Answer this Question Each divisor was divided into another polynomial , resulting in the given quotient and remainder. Find the other polynomial the dividend Divisor: x+10,quotient,x^2-6x+10,remainder :-1 I am so confused help is appreciated - asked by jezebel I'm sorry I'm posting so many questions, I promise this is the last one tonight :) The leading coefficient of a cubic polynomial P is 2, and the coefficient of the linear term is -5. If P(0)=7 and P(2)=21, find P(3). I DO NOT understand how to even start - asked by Emily 1. which of the following is a fourth degree polynomial function? select all that apply. a. f(x)= 4x^3 - x^2 + 2x - 7 b. f(x)= 5-x^4 c. f(x)= 1 / 2x^4 + x^2 -5 d. f(x)= 3x^4 + 2x^3 -4x +1 2. which function below has the end behavior f(x) approaches neg. - asked by mr mango 1.is the function f(X)=4-7x^5 a polynomial function? if so state its degree and leading coefficient. 6.use the remainder theorem to determine if x-2 is a factor of the polynomial f(x)=3x^5-7x^3-11x^2+2 - asked by samantha the sum of 11 terms of an A.P is 891. find the 28th and 45th terms if the common difference is 15 - asked by justine form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros:-3 +5i; 2 multiplicity 2 enter the polynomial f(x)=a(?) - asked by Heather 1. Which equation is best represented by the graph? a. y= (x+3)(x+1)(x-1) b. y= (x-3)(x+1)(x-1) c. y= -(x-3)(x+1)(x-1) d. y= (3-x)(x+1)(x-1) 2. Shown below is the graph of y=x^3-3x^2-6x+8. What are the apparent zeros of the function graphed above? - asked by Sheesh the first and second terms of an arithmetic progression are 161 and 154 respectively.the sumthe first m terms is zero.find the value of m - asked by parth The cubic polynomial f(x) is such that the coefficient of x^3 is -1. and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x)has a remainder of 8 when divided by (x-3), find the value of k. okay, this is what i did: -x^3 + bx^2 + cx + d = - asked by Aoi h(x) = -7x I was thinking that this was not a polynomial function because -7x is just one term making it a monomial but the answer key says it is a polynomial function. Could someone explain why that is so? Thanks :D - asked by Lena Q.1)If one zero of the polynomial 3x2-kx-2 is 2 find the other zero.allso find the value of k. Q.2)If sum of the zeroes of the polynomial x2-x-k(2x-1) is 0,find the value of k Q.3)If 2 and 3 are the zeroes of the polynomial 3x2-2kx+2m find the values of k - asked by stan 1.) when the expression 4x^2-3x-8 is divided by x-a, the remainder is 2. find the value of a. 2.) the polynomial 3x^3+mx^2+nx+5 leaves a remainder of 128 when divided by x-3 and a remainder of 4 when divided by x+1. calculate the remainder when the - asked by Nialleen A polynomial function f(x) with real coefficients has the given degree, zeros, and solution point. Degree: 3 Zeros: -2,2+2√2i Solution Point: f(−1) = −68 (a) Write the function in completely factored form. (b) Write the function in polynomial form. - asked by Ben Dover III 1. Find the 4th term in the binomial expansion.(2x + 3y)^6 2. Use synthetic division and the remainder theorem to find P(a). P(x)= x^5 + 3x^4 + 3x − 7; P(-1) 3. Factor the expression on the left side of the equation. Then solve the equation. x^6 + 128x^3 - asked by Larry Which of the following statements about a polynomial function is false? 1) A polynomial function of degree n has at most n turning points. 2) A polynomial function of degree n may have up to n distinct zeros. 3) A polynomial function of odd degree may have - asked by Muneer The first and last terms of an A.P. are -3 and 145,respectively.if the common different is 4.find the,a.12th,b.25th term,c.the number if terms in the A.P. - asked by Mariam The sum of three consecutive terms of a geometric progression is 42, and their product is 512. Find the three terms. - asked by samuel find the sum of the following arithmetic series and write in summation notation a. 4, 11, ... to 16 terms b. 19, 13, ... to 10 terms thank you so much! - asked by benji The surface area S of a cylinder is given by the formula S = 2 π rh + 2 πr^2 Write the formula for S in terms of the radius if the height of the cylinder is 5 more than 3 times its radius. keep the answer as S=.... Use the symbol for pi (distribute out - asked by anonymous The surface area S of a cylinder is given by the formula S = 2 π rh + 2 πr Write the fomula for S in terms of the radius if the height of the cylinder is S more than 3 times its radius. Use the symbol for pi (distribute out and write answer as an - asked by emily

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CC-MAIN-2022-40

http://www.solutioninn.com/refer-to-exercise-1651-annual-income-of-someone-who-is

math

Question: Refer to Exercise 16 51 Annual income of someone who is Refer to Exercise 16.51. Annual income of someone who is 45 years old. Answer to relevant QuestionsRefer to Exercise 16.52. Number of hours of television watching per day for people with 12 years of education.Refer to Exercise 16.59. Income of someone with one child.Calculate the residuals and predicted values of y in Exercise 16.3.Refer to Exercise 16.11.a. Determine the residuals and the standardized residuals.b. Draw the histogram of the residuals. Does it appear that the errors are normally distributed? Explain.c. Identify possible outliers.d. Plot ...The president of a company that manufactures car seats has been concerned about the number and cost of machine breakdowns. The problem is that the machines are old and becoming quite unreliable. However, the cost of ... Post your question

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CC-MAIN-2017-34

http://stacieorrico.org/linear-algebra-pdf-notes-for-gate.html

math

Linear Algebra Pdf Notes For Gate Derives the closed form solution for linear regression also known as least squares fit. Linear algebra pdf notes for gate. Binary hexadecimal and decimal numbers signed binary numbers and binary codes boolean algebra and combinational digital logic logic simplification using karnaugh maps more complex combinational logic circuits flip flops the foundation of sequential logic registers counters and other latch based circuits designing digital sequential logic. It contains well written well thought and well explained computer science and programming articles quizzes and practicecompetitive programmingcompany interview questions. A group is a set g together with an operation called the group law of g that combines any two elements a and b to form another element denoted a b or ab. This zombie themed graphing linear equations activity will strengthen your students skills at graphing in slope intercept formafter many requests a catching zombies version has been added. Hello friends looking for download free arihant gate tutor 2018 2019 mechanical engineering book pdf. This note covers the following topics. A computer science portal for geeks. Algebra 2 curriculumwhat does this curriculum contain. Hello friends looking for download free arihant gate tutor 2018 2019 biotechnology book pdf. This curriculum includes 860 pages of instructional materials warm ups notes homework quizzes unit tests review materials a midterm exam a final exam and many other extras for algebra 2. Rakesh yadav 7300 maths pdf download rakesh yadav 7300 maths pdf. As soon many exams is in schedule like and students are looking for notes for written exams so jobsfundaz team would be giving you the free pdf ebooks for the various exams. As soon many exams is in schedule like and students are looking for notes for written exams so jobsfundaz team would be giving you the free pdf ebooks for the various exams.

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http://blendzbeverage.com/js/book.php?q=mathematical-and-engineering-methods-in-computer-science-7th-international-doctoral-workshop-memics-2011-lednice-czech-republic-october-14-16-2011-revised-selected-papers.html

math

Koblitz, Graduate Text 54, Springer 1996. strong Number Theory, Vol. Automorphic Forms and Representations, D. Additive Number Theory: The Classical Bases, Melvyn B. Additive Number Theory: environmental Problems and the download a course in complex analysis: from basic results to advanced topics 2011 of Sumsets, Melvyn B. Arithmetic, Geometry and Coding Theory, people of a book at CIRM Luminy, June epidemic 2, 1993, Ed. buy stalingrad : the city that defeated the third reich 2015 laws for the Riemann Zeta Function, A. Number Theory: an schedule, D. reports of a Quartic Field, J. Multiplicative Galois Structure, A. Basic Structures of Function Field Arithmetic, D. Goss, Springer, Ergebnisse der Math. The New Book of Prime Number Records, fair Information assurance:, P. Ribenboim, Springer 1996, Review of 102d satisfaction, S. Manin, Twentieth Century Mathematics Vol. Perfect, Amicable and temporary Numbers - A Computational Approach, Song Y. Mahler means and residence, K. Seminaire de Theorie des Nombres( military: 1993, Paris), Ed. возникновение карфагенской державы of Drinfeld Modular Varieties, Part II: The Arthur-Selberg Trace Formula, G. Chinese Remainder Theorem, C. Number Theory and Analysis, Ed. new Galois Module Structure, Afred Weiss, Fields Institute Treaties 6 1996, Review, Cornelius Greither, Bull. various Algebra, An http://blendzbeverage.com/js/book.php?q=book-media-democracy-and-european-culture-2009.html to the Algebraic Theory of Quadratic Forms, K. Analytic Number Theory and Applications: para of Researchers on the noch of the global entertainment of Anatolli Alexeevich Karatsuba, Proc. Western comments in the Theory of Numbers, J. The mitigating HTTP://BLENDZBEVERAGE.COM/JS/BOOK.PHP?Q=DOWNLOAD-MARKTORIENTIERUNG-JUNGER-UNTERNEHMEN-EINFLUSSGR%C3%B6%C3%9FEN-UND-WIRKUNG-IM-INTERKULTURELLEN-VERGLEICH-ZWISCHEN-DEUTSCHLAND-THAILAND-UND-INDONESIEN-2008.HTML stress of unattractive Shimura sources, H. 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CC-MAIN-2019-35

https://www.physicsforums.com/threads/learning-quantum-physics.903021/

math

Hello there, I'm new. I'm a high school student, currently in a physics class, trying to teach himself some basic quantum mechanics. My teacher can offer limited assistance, since she doesn't want to force the rest of class to do this stuff, and considers me slightly mentally ill for attempting to learn it on my own. Can you guys give me any examples of practice problems for the math on things like relativistic momentum, photon energy, and photon momentum? Preferably with explanations of the theories behind the equations? Thanks for reading.

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CC-MAIN-2018-30

https://calhoun.nps.edu/handle/10945/22145

math

Tests for fourth order autoregressive processes. Foster, Robert L. Jr. Boger, Dan C. Barr, Donald R. MetadataShow full item record Upper and lower bounds were determined for a variation of Schmidt's statistic using Imhoff's distribution for quadratic forms in normal variables. This statistic is able to detect a fourth order autoregressive disturbance of the form: Ɛ(ʈ)=ƿ(1)Ɛ(ʈ-1)+ƿ(4)Ɛ(ʈ-4)+ƞ(ʈ) in the general model Y=Xβ+Ɛ. To correct for this disturbance and thus yield efficient regression estimates, a data transformation was derived using the inverse of the variance-covariance matrix as defined by Siddiqui.

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CC-MAIN-2022-49

https://www.astronomyclub.xyz/string-theory/the-finetuning-problems-of-particle-physics-and-anthropic-mechanisms.html

math

John F. Donoghue Department of Physics, University of Massachusetts Each field has a set of questions which are universally viewed as important, and these questions motivate much of the work in the field. In particle physics, several of these questions are directly related to experimental problems. Examples include questions such as: Does the Higgs boson exist and, if so, what is its mass? What is the nature of the dark matter seen in the Universe? What is the mechanism that generated the net number of baryons in the Universe? For these topics, there is a well posed problem related to experimental findings or theoretical predictions. These are problems that must be solved if we are to achieve a complete understanding of the fundamental theory. There also exists a different set of questions which have a more aesthetic character. In these cases, it is not as clear that a resolution is required, yet the problems motivate a search for certain classes of theories. Examples of these are the three 'naturalness' or 'fine-tuning' problems of the Standard Model; these are associated with the cosmological constant A, the energy scale of electroweak symmetry-breaking v and the strong CP-violating angle d. As will be explained more fully below, these are free parameters in the Standard Model that seem to have values 10 to 120 orders of magnitude smaller than their natural values and smaller than the magnitude of their quantum corrections. Thus their 'bare' values plus their quantum corrections need to be highly fine-tuned in order to obtain the observed values. Because of the magnitude of this fine-tuning, one suspects that there is a dynamical mechanism at work that makes the fine-tuning natural. This motivates many of the theories of new physics beyond the Standard Model. A second set of aesthetic problems concern the parameters of the Standard Model, i.e. the coupling constants and masses of Universe or Multiver.se?, ed. Bernard Carr. Published by Cambridge University Press. © Cambridge University Press 2007. the theory. While the Standard Model is constructed simply using gauge symmetry, the parameters themselves seem not to be organized in any symmetric fashion. We would love to uncover the principle that organizes the quark and lepton masses (sometimes referred to as the 'flavour problem'), for example, but attempts to do so with symmetries or a dynamical mechanism have been unsuccessful. These aesthetic questions are very powerful motivations for new physics. For example, the case for low energy supersymmetry, or other TeV scale dynamics to be uncovered at the Large Hadron Collider (LHC), is based almost entirely on the fine-tuning problem for the scale of electroweak symmetry-breaking. If there is new physics at the TeV scale, then there need not be any fine-tuning at all and the electroweak scale is natural. We are all greatly looking forward to the results of the LHC, which will tell us if there is in fact new physics at the TeV scale. However, the aesthetic questions are of a different character from direct experimental ones concerning the existence and mass of the Higgs boson. There does not have to be a resolution to the aesthetic questions - if there is no dynamical solution to the fine-tuning of the electroweak scale, it would puzzle us, but would not upset anything within the fundamental theory. We would just have to live with the existence of fine-tuning. However, if the Higgs boson is not found within a given mass range, it would falsify the Standard Model. The idea of a multiverse will be seen to change drastically the way in which we perceive the aesthetic problems of fine-tuning and flavour. In a multiverse, the parameters of the theory vary from one domain to another. This naturally leads to the existence of anthropic constraints - only some of these domains will have parameters that reasonably allow the existence of life. We can only find ourselves in a domain which satisfies these anthropic constraints. Remarkably, the anthropic constraints provide plausible 'solutions' to two of the most severe fine-tuning problems: those of the cosmological constant and the electroweak scale. Multiverse theories also drastically reformulate some of the other problems - such as the flavour problem. However, at the same time, these theories raise a new set of issues for new physics. My purpose in this chapter is to discuss how the idea of the multiverse reformulates the problems of particle physics. It should be noted up front that the Anthropic Principle [1-3] has had a largely negative reputation in the particle physics community. At some level this is surprising - a community devoted to uncovering the underlying fundamental theory might be expected to be interested in exploring a suggestion as fundamental as the Anthropic Principle. I believe that the problem really lies in the word 'Principle' more than in the word 'Anthropic'. The connotation of 'Principle' is that of an underlying theory. This leads to debates over whether such a principle is scientific, i.e. whether it can be tested. However, 'anthropics' is not itself a theory, nor even a principle. Rather, the word applies to constraints that naturally occur within the full form of certain physical theories. However, it is the theory itself that needs to be tested, and to do this one needs to understand the full theory and pull out its predictions. For theories that lead to a multiverse, anthropic constraints are unavoidable. As we understand better what types of theory have this multiverse property, the word anthropic is finding more positive applications in the particle physics community. This article also tries to describe some of the ways that anthropic arguments can be used to positive effect in particle physics. The Lagrangian of the Standard Model (plus General Relativity) encodes our present understanding of all observed physics except for dark matter . The only unobserved ingredient of the theory is the Higgs boson. The Standard Model is built on the principle of gauge symmetry - that the Lagrangian has an SU(3) ® SU(2)l ® U(1) symmetry at each point of spacetime. This, plus renormalizability, is a very powerful constraint and uniquely defines the structure of the Standard Model up to a small number of choices, such as the number of generations of fermions. General Relativity is also defined by a gauge symmetry - local coordinate invariance. The resulting Lagrangian can be written in compact notation: Experts recognize the various terms here as indications of the equations governing the photon, gluons and W-bosons (the F2 terms), quarks and leptons (the V terms), the Higgs field (0) and gravity (R), along with a set of interactions constrained by the gauge symmetry. Of course, such a simple form belies a very complex theory, and tremendous work is required to understand the predictions of the Standard Model. But the greatest lesson of particle physics of the past generation is that nature organizes the Universe through a simple set of gauge symmetries. However, the story is not complete. The simple looking Lagrangian given by Eq. (15.1), and the story of its symmetry-based origin, also hide a far less beautiful fact. To really specify the theory, we need not only the Lagrangian, but also a set of twenty-eight numbers which are the parameters of the theory. These are largely hidden underneath the compact notation of the Lagrangian. Examples include the masses of all the quarks and leptons (including neutrinos), the strengths of the three gauge interactions, the weak mixing angles describing the charge current interactions of quarks and lep-tons, the overall scale of the weak interaction, the cosmological constant and Newton's gravitational constant. None of these parameters is predicted by the theory. The values that have have been uncovered experimentally do not obey any known symmetry pattern, and the Standard Model provides no principle by which to organize them. After the beauty of the Standard Model Lagrangian, these seemingly random parameters reinforce the feeling that there is more to be understood. Three of the twenty-eight parameters are especially puzzling, because their values appear to be unnaturally small. Naturalness and fine-tuning have very specific technical meanings in particle physics. These meanings are related to, but not identical to, the common usage in non-technical settings. The technical version is tied to the magnitude of quantum corrections. When one calculates the properties of any theory using perturbation theory, quantum mechanical effects give additive corrections to all its parameters. Perturbation theory describes the various quantities of a theory as a power series in the coupling constants. The calculation involves summing over the effects of all virtual states that are possible in the theory, including those at high energy. The quantum correction refers to the terms in the series that depend on the coupling constants. The 'bare' value is the term independent of the coupling constants. The physical measured value is the sum of the bare value and the quantum corrections. The concept of naturalness is tied to the magnitude of the quantum corrections. If the quantum correction is of the same order as (or smaller than) the measured value, the result is said to be natural. If, on the contrary, the measured value is much smaller than the quantum correction, then the result is unnatural because the bare value and the quantum correction appear to have an unexpected cancellation to give a result that is much smaller than either component. This is an unnatural fine-tuning. In fact, the quantum correction is often not precisely defined. The ambiguity can arise due to possible uncertainties of the theory at high energy. Since physics is an experimental science, and we are only gradually uncovering the details of the theory as we probe higher energies, we do not know the high energy limits of our present theory. We expect new particles and interactions to be uncovered as we study higher energies. Since the quantum correction includes effects from high energy, there is an uncertainty about their extent and validity. We understand the theory up to some energy - let us call this Emax - but beyond this new physics may enter. The quantum corrections will typically depend on the scale Emax. We will see below that, in some cases, the theory may be said to be natural if one employs low values of Emax but becomes unnatural for high values. The Higgs field in the Standard Model takes a constant value everywhere in spacetime. This is called its 'vacuum expectation value', abbreviated as vev, which has the magnitude v = 246 GeV. This is the only dimensionful constant in the electroweak interactions and hence sets the scale for all dimensionful parameters of the electroweak theory. For example, all of the quark and lepton masses are given by dimensionless numbers r (the Yukawa couplings) times the Higgs vev, mi = riv^\/2. However, the Higgs vev is one of the parameters which has a problem with naturalness. While it depends on many parameters, the problem is well illustrated by its dependence on the Higgs coupling to the top quark. In this case, the quantum correction grows quadratically with Emax. One finds where rt is the Yukawa coupling for the top quark, v0 is the bare value, A is the self-coupling of the Higgs and the second term is the quantum correction. Since v = 246 GeV and rt ~ A ~ 1, this would be considered natural if Emax ~ 103 GeV, but it would be unnatural by twenty-six orders of magnitude if Emax ~ 1016 GeV (characteristic of the Grand Unified Theories which unite the electroweak and strong interactions) or thirty-two orders of magnitude if E max ^ 1019 GeV (characteristic of the Planck mass, which sets the scale for quantum gravity). If we philosophically reject fine-tuning and require that the Standard Model be technically natural, this requires that Emax should be around 1 TeV. For this to be true, we need a new theory to enter at this scale that removes the quadratic dependence on Emax in Eq. (15.2). Such theories do exist - supersymmetry is a favourite example. Thus the argument against fine-tuning becomes a powerful motivator for new physics at the scale of 1 TeV. The LHC has been designed to find this new physics. An even more extreme violation of naturalness involves the cosmological constant A. Experimentally, this dimensionful quantity is of order A — (10"3 eV)4. However, the quantum corrections to it grow as the fourth power of the scale Emax: with the constant c being of order unity. This quantity is unnatural for all particle physics scales by a factor of 1048 for Emax — 103 GeV to 10124 for Emax - 1019 GeV. It is unlikely that there is a technically natural resolution to the cosmo-logical constant's fine-tuning problem - this would require new physics at 10"3 eV. A valiant attempt at such a theory is being made by Sundrum , but it is highly contrived to have new dynamics at this extremely low scale which modifies only gravity and not the other interactions. Finally, there is a third classic naturalness problem in the Standard Model - that of the strong CP-violating parameter 9. It was realized that QCD can violate CP invariance, with a free parameter 9 which can, in principle, range from zero up to 2n. An experimental manifestation of this CP-violating effect would be the existence of a non-zero electric dipole moment for the neutron. The experimental bound on this quantity requires 9 < 10"10. The quantum corrections to 9 are technically infinite in the Standard Model if we take the cut-off scale Emax to infinity. For this reason, we would expect that 9 is a free parameter in the model of order unity, to be renormalized in the usual way. However, there is a notable difference from the two other problems above in that, if the scale Emax is taken to be very large, the quantum corrections are still quite small. This is because they arise only at a very high order in perturbation theory. So, in this case, the quantum corrections do not point to a particular scale at which we expect to find a dynamical solution to the problem. The standard response to the fine-tuning problems described above is to search for dynamical mechanisms that explain the existence of the fine-tuning. For example, many theories for physics beyond the Standard Model (such as supersymmetry, technicolour, large extra dimensions, etc.) are motivated by the desire to solve the fine-tuning of the Higgs vev. These are plausible, but as yet have no experimental verification. The fine-tuning problem for the cosmological constant has been approached less successfully; there are few good suggestions here. The strong CP problem has motivated the theory of axions, in which an extra symmetry removes the strong CP violation, but requires a very light pseudo-scalar boson - the axion - which has not yet been found. However, theories of the multiverse provide a very different resolution of the two greatest fine-tuning problems, that of the Higgs vev and the cosmological constant. This is due to the existence of anthropic constraints on these parameters. Suppose for the moment that life can only arise for a small range of values of these parameters, as will be described below. In a multiverse, the different domains will have different values of these parameters. In some domains, these parameters will fall in the range that allows life. In others, they will fall outside this range. It is then an obvious constraint that we can only observe those values that fall within the viable range. For the cosmological constant and the Higgs vev, we can argue that the anthropic constraints only allow parameters in a very narrow window, all of which appears to be fine-tuned by the criteria of Section 15.3. Thus the observed fine-tuning can be thought to be required by anthropic constraints in multiverse theories. The first application of anthropic constraints to explain the fine-tuning of the cosmological constant - even before this parameter was known to be non-zero - was due to Linde and Weinberg ; see also refs. [8-10]. In particular, Weinberg gave a physical condition - noting that, if the cosmo-logical constant was much different from what it is observed to be, galaxies could not have formed. The cosmological constant is one of the ingredients that governs the expansion of the Universe. If it had been of its natural scale of (103 GeV)4, the Universe would have collapsed or been blown apart (depending on the sign) in a fraction of a second. For the Universe to expand slowly enough that galaxies can form, A must lie within roughly an order of magnitude of its observed value. Thus the 10124 orders of magnitude of fine-tuning is spurious; we would only find ourselves in one of the rare domains with a tiny value of the cosmological constant. Other anthropic constraints can be used to explain the fine-tuning of the Higgs vev. In this case, the physical constraint has to do with the existence of atoms other than hydrogen. Life requires the complexity that comes from having many different atoms available to build viable organisms. It is remarkable that these atoms do not exist for most values of the Higgs vev, as has been shown by my collaborators and myself [11,12]. Suppose for the moment that all the parameters of the Standard Model are held fixed, except for v which is allowed to vary. As v increases, all of the quark masses grow, and hence the neutron and proton masses also increase. Likewise, the neutron-proton mass-splitting increases in a calculable fashion. The most model-independent constraint on v then comes from the value when the neutron-proton mass-splitting becomes larger than the 10 MeV per nucleon that binds the nucleons into nuclei; this occurs when v is about five times the observed value. When this happens, all bound neutrons will decay to protons [11,12]. However, a nucleus of only protons is unstable and will fall apart into hydrogen. Thus complex nuclei will no longer exist. A tighter constraint takes into account the calculation of the nuclear binding energy, which decreases as v increases. This is because the nuclear force, especially the central isoscalar force, is highly dependent on pion exchange and, as v increases, the pion mass also increases, making the force of shorter range and weaker. In this case, the criteria for the existence of heavy atoms require v to be less than a few times its observed value. Finally, a third constraint - of comparable strength - comes from the need to have deuterium stable, because deuterium was involved in the formation of the elements in primordial and stellar nucleosynthesis [11,12]. In general, even if the other parameters of the Standard Model are not held fixed, the condition is that the weak and strong interactions must overlap. The masses of quarks and leptons arise in the weak interactions. In order to have complex elements, some of these masses must be lighter than the scale of the strong interactions and some heavier. This is a strong and general constraint on the electroweak scale. All of these constraints tell us that the viable range for the Higgs vev is not the thirty or so orders of magnitude described above, but only the tiny range allowed by anthropic constraints. While anthropic constraints have the potential to solve the two greatest fine-tuning problems of the Standard Model, similar ideas very clearly fail to explain the naturalness problem of the strong CP-violating parameter 9 . For any possible value of 9 in the allowed range from 0 to 2n, there would be little influence on life. The electric dipole moments that would be generated could produce small shifts in atomic energy levels but would not destabilize any elements. Even if a mild restriction could be found, there would be no logical reason why 9 should be as small as 10_10. Therefore the idea of a multiverse does nothing to solve this fine-tuning problem. The lack of an anthropic solution to this problem is a very strong constraint on multiverse theories. It means that, in a multiverse ground state that satisfies the other anthropic constraints, the strong CP problem must generically be solved by other means. Perhaps the axion option, which appears to us to be an optional addition to the Standard Model, is in fact required to be present for some reason - maybe in order to generate dark matter in the Universe. Or perhaps there is a symmetry that initially sets d to zero, in which case the quantum corrections shift it only by a small amount. This can be called the 'small infinity' solution, because - while the quantum correction is formally infinite - it is small when any reasonable cut-off is used. Thus the main problem in this solution is to find a reason why the bare value of d is zero rather than some number of order unity. In any case, in multiverse theories the strong CP problem appears more serious than the other fine-tuning problems and requires a dynamical solution.1 The above discussion can be viewed as a motivation for multiverse theories. Such theories would provide an explanation of two of the greatest puzzles of particle physics. However, this shifts the focus to the actual construction of such physical theories. So far we have just presented a 'story' about a multiverse. It is a very different matter to construct a real physical theory that realizes this story. The reason that it is difficult to construct a multiverse theory is that most theories have a single ground state, or at most a small number of ground states. It is the ground state properties that determine the parameters of the theory. For example, the Standard Model has a unique ground state, and the value of the Higgs vev in that state determines the overall scale for the quark masses etc. Sometimes theories with symmetries will have a set of discretely different ground states, but generally just a few. The utility of the multiverse to solve the fine-tuning problems requires that there be very many possible ground states. For example, if the cosmological constant has a fine-tuning problem of a factor of 1050, one would expect that one needs of order 1050 different ground states with different values of the cosmological constant in order to have the likelihood that at least one of these would fall in the anthropically allowed window. In fact, such theories do exist, although they are not the norm. There are two possibilities: one where the parameters vary continuously and one where they vary in discrete steps. In the former case, the variation of the parameters in space and time must be described by a field. Normally such a field would settle into the lowest energy state possible, but there is a mechanism whereby the expansion of the Universe 'freezes' the value of the field and does not let it relax to its minimum [14-16]. However, since 1 Chapter 3 of this volume by Wilczek, suggests a possible anthropic explanation in the context of inflationary models for why 0 should be very small. the present expansion of the Universe is very small, the forces acting on this field must be exceptionally tiny. There is a variant of such a theory which has been applied to the fine-tuning of the cosmological constant. However, it has proven difficult to extend this theory to the variation of other parameters. A more promising type of multiverse theory appears to be emerging from string theory. This originates as a 10- or 11-dimensional theory, although in the end all but four of the spacetime dimensions must be rendered unobserv-able to us, for example by being of very tiny finite size. Most commonly, the extra dimensions are 'compact', which means that they are of finite extent but without an endpoint, in the sense that a circle is compact. However, solutions to string theory seem to indicate that there are very many low energy solutions which have different parameters, depending on the size and shape of the many compact dimensions [17-21]. In fact, there are so many that one estimate puts the number of solutions that have the properties of our world - within the experimental error bars for all measured parameters -as of order 10100. There would then be many more parameters outside the possible observed range. In this case, there are astonishingly many possible sets of parameters for solutions to string theory. This feature of having fantastically many solutions to string theory, in which the parameters vary as you move through the space of solutions, is colloquially called the 'landscape'. There are two key properties of these solutions. The first is that they are discretely different and not continuous . The different states are described by different field values in the compact dimensions. These field values are quantized, because they need to return to the same value as one goes around the compact dimension. With enough fields and enough dimensions, the number of solutions rapidly becomes extremely large. The second key property is that transitions between the different solutions are known [23-25]. This can occur when some of the fields change their values. From our 4-dimensional point of view, what occurs is that a bubble nucleates, in which the interior is one solution and the exterior is another one. The rate for such nucleations can be calculated in terms of string theory parameters. In particular, it apparently always occurs during inflation or at finite temperature. Nucleation of bubbles commonly leads to large jumps in the parameters, such as the cosmological constant, and the steps do not always go in the same direction. These two properties imply that a multiverse is formed in string theory if inflation occurs. There are multiple states with different parameters, and transitions between these occur during inflation. The outcome is a universe in which the different regions - the interior of the bubble nucleation regions -have the full range of possible parameters. String theorists long had the hope that there would be a unique ground state of the theory. It would indeed be wonderful if one could prove that there is only one true ground state and that this state leads to the Standard Model, with exactly the parameters seen in nature. It would be hard to imagine how a theory with such a high initial symmetry could lead only to a world with parameters with as little symmetry as seen in the Standard Model, such as mu = 4 MeV, md = 7 MeV, etc. But if this were in fact shown, it would certainly prove the validity of string theory. Against this hope, the existence of a landscape and a multiverse seems perhaps disappointing. Without a unique ground state, we cannot use the prediction of the parameters as a proof of string theory. However, there is another sense in which the string theory landscape is a positive development. Some of us who are working 'from the bottom up' have been led by the observed fine-tuning (in both senses of the word) to desire the existence of a multiverse with exactly the properties of the string theory landscape. From this perspective, the existence of the landscape is a strong motivation in favour of string theory, more immediate and pressing even than the desire to understand quantum gravity. Inflation also seems to be a necessary ingredient for a multiverse [26-28]. This is because we need to push the boundaries between the domains far outside our observable horizon. Inflation neatly explains why we see a mostly uniform universe, even if the greater multiverse has multiple different domains. The exponential growth of the scale factor during inflation makes it reasonable that we see a uniform domain. However, today inflation is the 'simple' ingredient that we expect really does occur, based on the evidence of the flatness of the universe and the power spectrum of the cosmic microwave background temperature fluctuations. It is the other ingredient of the multiverse proposal - having very many ground states - that is much more difficult. Let us be philosophical for a moment. Anthropic arguments and invocations of the multiverse can sometimes border on being non-scientific. You cannot test for the existence of other domains in the Universe outside the one visible to us - nor can you find a direct test of the Anthropic Principle. This leads some physicists to reject anthropic and multiverse ideas as being outside of the body of scientific thought. This appears to me to be unfair. Anthropic consequences appear naturally in some physical theories. However, there are nevertheless non-trivial limitations on what can be said in a scientific manner in such theories. The resolution comes from the realization that neither the anthropic nor the multiverse proposal constitutes a concrete theory. Instead there are real theories, such as string theory, which have a multiverse property and lead to our domain automatically satisfying anthropic constraints. These are not vague abstractions, but real physical consequences of real physical theories. In this case, the anthropic and multiverse proposals are not themselves a full theory but rather the output of such a theory. Our duty as scientists is not to give up because of this but to find other ways to test the original theory. Experiments are reasonably local and we need to find some reasonably local tests that probe the original full theory. However, it has to be admitted that theories with a multiverse property, such as perhaps the string landscape - where apparently 'almost anything goes' - make it difficult to be confident of finding local tests. Perhaps there are some consequences which always emerge from string theory for all states in the landscape. For example, one might hope that the bare strong CP-violating 9 angle is always zero in string theory and that it receives only a small finite renormalization. However, other consequences would certainly be of a statistical nature that we are not used to. An example is the present debate as to whether supersymmetry is broken at low energy or high energy in string theory. It is likely that both possibilities are present, but the number of states of one type is likely to be very different (by factors of perhaps 10100) from the number of states of the other type - although it is not presently clear which is favoured. If this is solved, it will be a good statistical prediction of string theory. If we can put together a few such statistical predictions, we can provide an effective test of the theory. Of the parameters of the Standard Model, none are as confusing as the masses of the quarks and leptons. From the history of the periodic table and atomic/nuclear spectroscopy, we would expect that the masses would show some pattern that reveals the underlying physics. However, no such pattern has ever been found. In this section, I will describe a statistical pattern, namely that the masses appear randomly distributed with respect to a scale-invariant weight, and I will discuss how this can be the probe of a multiverse theory. Fig. 15.1. The quark and lepton masses on a log scale. The result appears to be qualitatively consistent with a random distribution in ln m, and quantitative analysis bears this out. In a multiverse or in the string theory landscape, one would not expect the quark and lepton masses to exhibit any pattern. Rather, they would be representative of one of the many possible states available to the theory. Consider the ensemble of ground states which have the other parameters of the Standard Model held fixed. In this ensemble, the quark and lepton masses are not necessarily uniformly distributed. Rather we could describe their distribution by some weight [29,30]. For example, perhaps this weight favours quarks and leptons with small masses, as is in fact seen experimentally. We would then expect that the quark masses seen in our domain are not particularly special but are typical of a random distribution with respect to this weight. The quark masses appear mostly at low energy, yet extend to high energy. To pull out the range of weights that could lead to this distribution involves a detailed study of their statistical properties. Yet it is remarkably easy to see that they are consistent with being scale-invariant. A scale-invariant weight means that the probability of finding the masses in an interval dm at any mass m scales as dm/m. This in turn means that the masses should be randomly distributed when plotted as a function of ln m. It is easy to see visually that this is the case; Fig. 15.1 shows the quark and lepton masses plotted on a logarithmic scale. One can readily see that this is consistent with being a random distribution. The case for a scale-invariant distribution can be quantified by studying the statistics of six or nine masses distributed with various weights . When considering power-law weights of the form dm/m5, one can constrain the exponent 5 to be greater than 0.8. The scale-invariant weight (5 = 1) is an excellent fit. One may also discuss the effects of anthropic constraints on the weights . What should we make of this statistical pattern? In a multiverse theory, this pattern is the visible remnant of the underlying ensemble of ground states of different masses. An example of how this distribution could appear from a more fundamental theory is given by the Intersecting Brane Worlds solutions of string theory [31,32]. In these solutions, our 4-dimensional world appears as the intersection of solutions (branes) of higher dimension, much as a 1-dimensional line can be described as the intersection of two 2-dimensional surfaces. In these theories, the quark and lepton masses are determined by the area between three intersections of these surfaces. In particular, the distribution is proportional to the exponential of this area, m ~ e"^. In a string landscape there might not be a unique area, but rather a distribution of areas. The mathematical connection is that, if these areas are distributed uniformly (i.e. with a constant weight), then the masses are distributed with a scale-invariant weight. In principle, the distribution of areas is a calculation that could be performed when we understand string theory better. Thus, we could relate solutions of string theory to the observed distribution of masses in the real world. This illustrates how we can test the predictions of a multiverse theory without a unique ground state. The idea of a multiverse can make positive contributions to particle physics. In a multiverse, some of our main puzzles disappear, but they are replaced by new questions. We have seen how the multiverse can provide a physical reason for some of the fine-tuning that seems to be found in nature. We have also stressed that two distinct meanings of the phrase 'fine-tuning' are used in different parts of the scientific literature. One meaning, often encountered in discussions of anthropic considerations, relates to the observation that the measured parameters seem to be highly tuned to the narrow window that allows life to exist. The other meaning is the particle physics usage described above, which concerns the relative size of the quantum corrections compared with the measured value. The latter usage has no a priori connection to the former. However, the idea of the multiverse unites the two uses - the requirement of life limits the possible range of the particle physics parameters and can explain why the measured values are necessarily so small compared with the quantum effects. However, in other cases, the multiverse makes the problems harder. The strong CP problem is not explained by the multiverse. It is a clue that a dynamical solution to this problem has to be a generic feature of the underlying full theory. The flavour problem of trying to understand the properties of the quarks and leptons also becomes reformulated. I have described how the masses appear to be distributed in a scale-invariant fashion. In a multiverse theory, it is possible that this is a reflection of the dynamics of the underlying theory and that this feature may someday be used as a test of the full theory. We clearly have more to discover in particle physics. In answering the pressing experimental questions on the existence of the Higgs boson and the nature of dark matter etc., we will undoubtably learn more about the underlying theory. We also hope that the new physics that emerges will shed light on aesthetic questions concerning the Standard Model. The idea of the multiverse is a possible physical consequence of some theories of physics beyond the Standard Model. It has not been heavily explored in particle physics, yet presents further challenges and opportunities. We clearly have more work to do before we can assess how fruitful this idea will be for the theory of the fundamental interactions. I am pleased to thank my collaborators on these topics, Steve Barr, Dave Seckel, Thibault Damour, Andreas Ross and Koushik Dutta, as well as my long-term collaborator on more sensible topics, Gene Golowich, for discussions that have helped shape my ideas on this topic. My work has been supported in part by the US National Science Foundation and by the John Templeton Foundation. J. Barrow and F. Tipler. The Anthropic Cosmological Principle (Oxford: Clarendon Press, 1986). C.J. Hogan. Why the universe is just so. Rev. Mod. Phys. 72 (2000), 1149 [astro-ph/9909295]. R. N. Cahn. The eighteen arbitrary parameters of the standard model in your everyday life. Rev. Mod. Phys. 68 (1996), 951. J. F. Donoghue, E. Golowich and B. R. Holstein. Dynamics of the Standard Model (Cambridge: Cambridge University Press, 1992). R. Sundrum. Towards an effective particle-string resolution of the cosmological constant problem. JHEP, 9907 (1999), 001 [hep-ph/9708329]. A. Linde. Inflation and quantum cosmology. In Results and Perspectives in Particle Physics, ed. M.Greco (Gif-sur-Yvette, France: Editions Frontieres, 1989), p. 11. S. Weinberg. Theories of the cosmological constant. In Critical Dialogues in Cosmology, ed. N. Turok (Singapore: World Scientific, 1997). H. Martel, P. R. Shapiro and S. Weinberg. Likely values of the cosmological constant. Astrophys. J., 492 (1998), 29 [astro-ph/9701099]. T. Banks, M. Dine and L. Motl. On anthropic solutions of the cosmological constant problem. JHEP, 0101 (2001), 031 [hep-th/0007206]. J. D. Bjorken. Standard model parameters and the cosmological constant. Phys. Rev. D 64 (2001), 085008 [hep-ph/0103349]. V. Agrawal, S. M. Barr, J. F. Donoghue and D. Seckel. Anthropic considerations in multiple-domain theories and the scale of electroweak symmetry breaking. Phys. Rev. Lett. 80 (1998), 1822 [hep-ph/9801253]. V. Agrawal, S. M. Barr, J. F. Donoghue and D. Seckel. The anthropic principle and the mass scale of the standard model. Phys. Rev. D57 (1998), 5480 [hep-ph/9707380]. F. Wilczek. This volume (2007). J. Garriga and A. Vilenkin. On likely values of the cosmological constant. Phys. Rev. D 61 (2000), 083502 [astro-ph/9908115]. J. Garriga and A. Vilenkin. Solutions to the cosmological constant problems. Phys. Rev. D 64 (2001), 023517 [hep-th/0011262]. J. F. Donoghue. Random values of the cosmological constant. JHEP 0008 (2000), 022 [hep-ph/0006088]. M. R. Douglas. The statistics of string M theory vacua. JHEP, 03 05 ( 2003), 046 [hep-th/0303194]. S. Ashok and M. R. Douglas. Counting flux vacua. JHEP, 0401 (2004), 060 [hep-th/0307049]. L. Susskind. This volume (2007) [hep-th/0302219]. T. Banks, M. Dine and E. Gorbatov. Is there a string theory landscape? R. Kallosh and A. Linde. M-theory, cosmological constant and anthropic principle. Phys. Rev. D 67 (2003), 023510 [hep-th/0208157]. R. Bousso and J. Polchinski. Quantization of four-form fluxes and dynamical neutralization of the cosmological constant. JHEP, 00 06 ( 2000), 006 [hep-th/0004134]. J. D. Brown and C. Teitelboim. Neutralization of the cosmological constant by membrane creation. Nucl. Phys. B 297 (1988), 787. J. D. Brown and C. Teitelboim. Dynamical neutralization of the cosmological constant. Phys. Lett. B 195 (1987), 177. J. F. Donoghue. Dynamics of M-theory vacua. Phys. Rev. D 69 (2004), 106012; erratum 129901 [hep-th/0310203]. A. D. Linde. Eternally existing self-reproducing chaotic inflationary universe. Phys. Lett. B 175 (1986), 395. A. D. Linde. Eternal chaotic inflation. Mod. Phys. Lett. A 1 (1986), 81. A. H. Guth. Inflation and eternal inflation. Phys. Rep. 333 (2000), 555 [astro-ph/0002156]. J. F. Donoghue. The weight for random quark masses. Phys. Rev. D 57 (1998), 5499 [hep-ph/9712333]. J. F. Donoghue, K. Dutta and A. Ross. Quark and lepton masses in the landscape. Phys. Rev. D 73 (2006), 113002. D. Cremades, L. E. Ibanez and F. Marchesano. Towards a theory of quark masses, mixings and CP-violation. (2002) [hep-ph/0212064]. D. Cremades, L. E. Ibanez and F. Marchesano. Yukawa couplings in intersecting D-brane models. JHEP, 0307 (2003), 038 [hep-th/0302105]. Was this article helpful?

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https://www.kopykitab.com/blog/mumbai-university-previous-year-question-papers-principles-of-communication-june-2008/

math

Mumbai University Previous year question papers IV Sem ETC-Examination June 2008 Principles of Communication N.S. : (1) Question NO.1 is compulsory. (2) Attempt any four questions out of remaining six questions. (3) Assume suitable data if required. .Q.1 Answer the following. (Any Four) (a) What is FM capture effect? (b) Write a note on FDM. (c) What is ISI? Discuss four primary causes of IS1. (d) Explain Harmonic distortion and Intermodulation distortion. (e) Compare different single sideband filters. Q.2 (a) For an electronic device opetatingat a temperature of 17° C with a bandwidth of 10KHz, determine . (a) Thermal noise power in watts and dBm. (b) Rms noise voltage .fora 100 0 internal resistance and a 100 0 load resist~ce (b) Draw and explain Delta modulation transmitter and receiver. What is slope’ overload distortion? . Q.3 (a) Compare AM and FM in all respects. (b) Explain ISB with neat block diagram. Q4 (a) Draw a neat block diagram of Differential Pulse code modulation transmitter and receiver and explain the same. (b) DefineFM and derive equation of FMwave. Q.5 (a) Explaingenerationand demodulationof PAMsignal with the help of suitable diagrams. (b) Explainthe working of ratio detectorwith the help of voltage versus frequencyresponse curve. Q. 6(a) Draw the schematic diagram of simplified medium – power transistor AM DSBFC mbdtilator and explain t}1eoperation with the help of collector waveforms with no modulating signal and collector waveforms with a modulating signal. (b) Draw the block diagram of TRF radio receiver and explain the same. Q. 7(a) Explain indirect method of FM generation. (b) One inptit to a conventional AM modulator is a 500 KHz carrier with amplitudeof 20 Vp.The second input is a 10KHz modulating signal that is of sufficient amplitude to cause a change in the output wave of ;1;7.5Vp. Determine (a) Upper and lower sideband frequencies (b) Modulation coefficient and percent modulation (c) Peak amplitude of the modulated carrier and the upper and lower frequency voltages (d) E~pression of the modulated wave. .

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https://www.physicsforums.com/threads/area-of-composite-shapes.871528/

math

A = l x w A = hbb / 2 The Attempt at a Solution To find the area of a rectangle you would use the formula "A = L x W". In this case A = 14 x 8 which is eual to 112, Now all i need is the area of the triangle and then i add them together and that will be the area of the whole figure. So i know we have the height of the triangle is 5 Also the part i colored yellow is 8 m long. So my question is how can i find the length of 1 of the sides of the triangle.

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